Q: if you found a dog 4 months ago and the owner is claiming him. will I have to give him back

A: You are in Tennessee, but here is what a court in Vermont said: "The value of a pet to its human companions has already been noted.   Accordingly, apart from providing care and shelter, finders of stray pets should also be encouraged to make every reasonable effort to find the animal's owner.   Although circumstances will vary, this might include contacting the local humane society, veterinarians, or the police department, posting notices near where the animal was found, and placing newspaper or radio advertisements.   Additionally, owners of lost pets should be enjoined to undertake reasonable efforts to locate their animals by contacting local humane societies and other appropriate agencies, printing and placing notices, or taking out appropriate advertisements.   Together these requirements provide an incentive to finders to care for stray pets and attempt to locate their owners, and place the onus on owners to conscientiously search for their pet."

http://caselaw.findlaw.com/vt-supreme-court/1488921.html

In that case, the lower court returned the dog to the original owner (the plaintiff) after one year. The Supreme Court affirmed this decision.

Assuming Tennessee courts would act the same way (and I don't see a reason why they wouldn't in general), I would say you should have to give the dog back. You were kind to take of the dog, but if the originally owner wants him back, you should return it.