is there a way to use the splitscreen on multiplayer server?

What do you mean?
When you want two log into the same server multiple times, you can't use the same user.
For that, you have to use a launcher, where you can log in with multiple accounts (like MultiMC) where you have to create (number of split-screens) versions and start Minecraft each with a different account.
In the End, LambdaControls enables you to use a specific controller for each Minecraft instance.

Hope that helps.