Bag drop off when connecting and switching terminals

Hello. I am landing at Terminal B from abroad and connecting onto a jetBlue flight departing from Terminal A. I am traveling with checked bags

Once I pick them up at the baggage claim, is there a place to drop them off in Terminal B? If so, where is it? Or do I need to take them with me on the Airtrain to Terminal A and drop them off there?

I will add that I am ariving on a codeshare flight so I should already be ticketed and with the correct baggage tags, and from my understanding will not need to go to the check in line at Terminal A.

Thank you!

EDIT - Forgot to specify I am ariving at Newark Airport.