Looking for information on Tn. Law when a man is married to one woman and is having a baby with another woman, must he adopt his own child

The biological parent has no need to adopt a child. They should be listed on the birth certificate. If they weren't they may need to get the birth certitifcate amended.

No he can be listed on the birth certificate or if the mother does not list him, have a paternity test to prove he is the father.

It is not possible to adopt your own child.

You may be married and sadly have children with a dozen different women you are still the father of each. And will have to pay child support

No, he does not have to adopt his own child. If his wife wants to raise the child as hers then she's the one who would have to do the adopting, provided of course that the mother consents.