Then, you need to re-do the birth certificate to make the place of birth consistent with the one in the passport if it is not convienent to make the change in the passport. Anyway, the birth certificate is very important document and the information should be consistent with the passport.
Of course, if the city your father was born was changed to another province, then you just need to explain it and not need to do the certificate again. For example, my hometown, Haikou City, orginally belonged to Guangdong Province, but now it belongs to Hainan Province, then I do not need to do my birth certificate again and just need to explain it.
