If you are in jail how do you go about adoption a girlfriend/boyfriends child?

You wait till you are released and married to them to do it.

If you jail would allow you to appear in civil court, normally you have to pay for your transportation and the guard expense. And honestly do you think the judge will want a person currently in jail to adopt, one of the things looked at for a adoptive parent

Next wile some do, most courts will still not adopt unless you are married to adopt a stepchild