If we get a divorce, will I have to pay child support for my step daughter who is from Jamaica?

You present two separate issues. You have not obligation for step children in a dissolution. I presume the child belongs to your other spouse. If you contracted to support someone else child, well that is different. The obligation is not from the marriage but from the contract.? The child can enforce the contract through a guardian (the other person in your marriage.) If the promise was for government purposes, again what is the relationship to the child.? Ending the marriage if the child is your spouse's ends the obligation.

It does not sound like you adopted her which would make you liable for child support. Seek the help if an immigration attorney regarding the paper you did sign.

Cannot answer without review of the document; generally you are only responsible if there was an adoption.

Then yes, you may have to pay child support. However, have your attorney look at the document. He or she may be able to figure a way around it.

You need to meet with an attorney and show that attorney "the paper" to see what your exposure is.