So here in I have a Climbing System allowing grabbable ledges and if anyone knows what can drive a curve via launch velocity i would like to know how it could be achieved?
Basically, there are two different solutions to your problem.
Set your jump and air control settings and then place your ledges so that you can reach them.
If your character is in a certain radius to your ledge, then grab the ledge. Use motion warping or similar to bridge the missing distance.
Predict where a climbable ledge is, if your character jumps then calculate the velocity needed to reach that point. For this you can use UGameplayStatics::SuggestProjectileVelocity.