When my son was born in 2010 me and his father was not married at the time 4 mt later we got married 2011 and the father name is not on the birth certificate dose the have any rights to my son

ANY question on law needs to include your general locale as laws vary by area.

Generally if you marry within a year of giving birth your husband becomes the presumed father. Even if you didn't marry, he has a father's rights by biology. He may have to go court to be declared the legal father to enforce his rights, but the rights are there.

Don't hear the term legitimate much any more, so not exactly sure what you mean by it,

But of course if he is the bio father of the child he has rights, he may have to file for his rights, is there a issue for it at this point ?