I am new to dramas and enjoing the diversity right now. But I found out that I love dramas in which a male character is either arrogant/cocky towards a girl,  enslaves her or is popular at school and falls surprisingly in love with the female character ... Sadly I've got the feeling that this type of drama isn't that popular and I don't even really know how that genre is called, so I'm asking you to help me find some nice dramas for me! :3

My absolute favorites are:

Those two are fitting my liking the best I think. I have also already seen the following dramas:

Can you maybe help me finding some similar dramas to my two favorites/the genre I prefer? And can you maybe even tell me how that genre I like is called? I am totally new to this and don't even know how I should search those dramas s:

Autumn's Concerto

Love O2O (althought he's more the type that is hugely popular and falls in love with a more normal student)

Secret Garden 

The Heirs (not only one, but two arrogant, dominating characters who fight over the girl)

Monstar

Flower boy ramhyun shop

Moorim school

Nodame Cantabile


Not set in school: greatest love, master sun, 1% of something, noble my love, falling for innocence

I think you mean male tsundere dramas? I love those shows too! I still follow the Kurosaki kun no Iinari ni Nante Naranai manga I'm addicted! 

If you haven't definitely watch the Thai versions of Itazura na Kiss called Kiss Me and Full House! Also the Taiwanese itazura It started with a kiss and They kiss Again. 

Other suggestions maybe try with male Tsundere type guys. Some of the girls are total pushover, clueless or they are stubborn pawns lol. Not all school dramas though.

Why Why love (same actors as Devil Beside You)(Taiwan girl becomes maid/slave of arrogant, immature, bad boy.)

Nodame's Cantabile (Japan ver) Naeil's Cantabile (Korean ver) (Arrogant, OCD guy and music prodigy meets unusual, messy female piano savant who falls desperately in love with him)

Hana yori Dango (Japan ver) Boys Over Flowers (Korean ver) Meteor Garden (Taiwan ver) Moon River (Taiwan loose adaptation)(Tough girl butts head with group of arrogant Prince like guys who rule private school.)

Fabulous Boys (Taiwanese ver), You're Beautiful (Korean ver), Ikemen desu ne (Japanese ver) (Girl about to become a nun has to masquerade as her incapacitated twin brother in popular idol band.)

Faith (Korean materialistic plastic surgeon is kidnapped by cold/serious royal guard captain and brought to the past.)

Hanazakari no Kimitachi e (Japan ver) To the beautiful you (Korean ver) Hana Kimi (Taiwan ver) (Girl disguises herself as a boy to attend all boys school and help encourage her depressed sports idol to recover.)

Yamato Nadeshiko Shichi Henge (Japanese horror loving girl moves into estate with four school Prince like guys who are tasked to turn her into a beautiful lady for free rent)

Stars Falling From The Sky (Korean spoiled girl chases after rich arrogant CEO when parents die in accident. Suddenly become guardian of several younger siblings sneaks them into CEO house where she becomes his maid.)

Liars Game (Japanese girl tricked into playing a high stacks game enlists the help of arrogant con man)

Love In Time (Hong Kong poor female student meets cold, cocky vampire)

Master Devil Do Not Kiss Me (Chinese A poor girl loses her mother and becomes ward of rich indebted family betrothed to arrogant, jerk son) 

Moon Lovers: Scarlet Heart Ryeo (Korean girl's soul is transported into the past where she becomes entangled with the lives of arrogant, cold, spoiled, etc princes)

My Amazing Boyfriend (Chinese Actress in near fatal car accident brings revives immortal corpse (cold and superior man) with blood. 

Goong/Princess Hours (Korean poor High school girl has to marry arrogant prince, who is in love with another girl, to help with family debts.)

The Heirs (Korean Poor girl has to move in mansion with rich boy and his family with secrets.)

Cinderella and Four Knights (Korean Poor girl is hired by the grandfather of three men to live with, help bring them together and teach them how to behave, the catch she can't date them) 

Personal taste (Korean Arrogant architect is misunderstood to be gay but continues with ruse to enter estate of girl desperate to pay debts)

Rooftop Prince (korean Superior Chosun dynasty prince and a four servants are transported to the modern world where they become dependant on poor hard working girl)

The Master's Sun (Korean greedy, arrogant CEO meets a Ghost attracting woman who finds him to be an oasis in her supernatural chaos)

The Legend of the blue sea (Korean arrogant con-artist meets a Mermaid)

ToGetHer (Taiwan idol loses popularity and is forced into cohabitation with manga obsessed girl)

Trot Lovers (Korean idol managing poor female singer to get career back)

W (Korean girl is pulled into graphic novel with mysterious arrogant lead

You Who Came from the Stars (Korean superior intelligent and cold immortal/alien man becomes entangled with a vain/materialistic but dimwitted beautiful actress/celebrity.)

Hope You Enjoy! :) 

I second Boys over flower or it's versions

a Bad boy/bully arrogant guy falls in love with female who is tough and stands up for herself. it do have a love triangle tho but i loved it! it's good! <3 ^^

I agree with the recs above. I'll add the following (note: I prefer dramas where the guy falls first + hard, so most of these have that dynamic even if the guy is arrogant at first):

  • Weightlifting Fairy Kim Bok Joo - ML is a popular swimming major, but not overly arrogant, especially after he recognizes the FL from his childhood
  • Imperial Doctress - one of the MLs / romantic interests enslaves the FL
  • Attention, Love! - ML is popular in school because of his looks and because he's the top student, sometimes he comes across as cold or aloof 
  • Sassy Go Go - ML is the top student in school; sometimes he's arrogant, but most of the time he's just intrigued by the FL

Also somewhat similar to your request:

  • Love in the Moonlight - ML is the arrogant crown prince and, although he doesn't enslave the FL, he is responsible for preventing her from escaping the palace so that she has to continue to pretend to be a eunuch (at this point he doesn't realize she's a girl and they have an amusing antagonistic relationship)
  • Sound of the Desert - at one point the ML essentially kidnaps the FL to keep her from running away
  • Princess Agents - FL is a maid in the ML's household, and he prevents her from running away

Forced marriage:

  • Empress Ki - again, not outright enslavement, but one of the MLs forces the FL to marry him and it's pretty much a form of slavery
  • The King's Woman - pretty much the same as Empress Ki
  • The Eternal Love - somewhat similar to the above - the FL is a girl from modern times whose soul shares the body of a girl in ancient times who has an arranged marriage with a prince

You should definitely watch Hana YoriDango this is one of the most representative ones withtin this genre and one of the most famous. Is my all time favorite jdrama!

Other recommendations:

  • Hana Kimi
  • Nodame Cantabile
  • Clover (it's not set in school is set on a working environment)
  • Delightful Girl, Choon Hyang
  • Kimi ni todoke
  • Fated to Love you (also not set in school)
  • Goong
  • Heartstrings
  • Full House (also not set in school)
  • Can Love become Money (also not set in school)