God's Gift: 14 Days (2014)

Both dramas feature time travel - character goes back to a certain moment in the past and is given a chance to prevent a death from happening while figuring out what is behind it.

Both dramas are thriller mysteries that will keep you hooked on the storyline from the start. I'll let you judge the rest, but if you enjoy one, you’ll likely enjoy the other as well.
Including [Voice Season 3]

Both dramas feature the same actor in the lead role. In "God's Gift," he plays an ex-cop, while in "Stranger," he portrays a prosecutor. Though their storylines are completely different, both are thriller mysteries that will keep you hooked with their suspense.
Including [Stranger Season 2]

It's as thrilling as this drama and they have their own mystery they have to solve as well. Both are also about time travel.

Similar story of parent trying everything to save the child with a mystery plot slowly revealing

Both dramas have to do with a parent saving their child within 2 weeks/14 days..

Both stories tell that of a child's kidnapping case and a mother who takes action to solve the case on her own.

The entire drama flows along with a string of mysteries and everyone seems suspicious except the leads (as usual).

In both stories the parent is given a chance to save their child by traveling back in time

Both dramas are intense, with fast moving plot filled with action as they both fight the time limit given to solve the mystery and defeat their opponent. You won't regret watching them!

Both are time warp dramas where the male and female leads are given multiple opportunities, based on changing events, to save someone’s life before tragedy happens.

If you want more of Cho Seung Woo in a time-bending fantasy-mystery adventure, then check this out. One has more sci-fi elements and the other has more of a crime drama feel to it, but if you're solely in it for CSW playing a charming smart-ass, then here you go.

from the trailer both seem like time traveling mystery crime dramas about people trying to find justice through time

Both dramas are crime show where people get a second chance to fight against their destiny, thanks to time travel. Both dramas are hard to predict and have twist plot.

Not only does the main female protagonist care deeply for their child, they both feel deeply to bring justice to the world and shut criminals away. They also have their detective male leads who would rather run to their side than chase after a criminal.