[fifi2020]

I have recently had to do a dna test as my sons father had requested one. I need to know if he can now take me to court to have his name on my sons birth certificate? Also I need to write a will stating who I want my son to go to when that time comes and if his father could contest that will?

[GV70]

i need to know if he can now take me to court to have his name on my sons birth certificate?

Short answer-YES.

Also i need to write a will stating who i want my son to go to when that time comes and if his father could contest that will?

Yes he can contest that will.
Generally parents have superior rights .Example from Michigan:
Presumption in favor of natural parents
1. The Michigan and U.S. Constitutions and existing case law give constitutional rights to natural parents for the custody of their own children. These rights can only be lost if facts exist indicating that the parents are not fit.
2. In effect, a strong presumption exists in favor of custody of children being with their own natural parents, as compared to being with the third party. The courts believe, based upon evidence from child psychologists, that it is in the best interests of children to be with their own parents.
3. This is so even
• when the third party may be a decent person or being able to be a good parent, or
• when arguably even when the third party could be a better custodial person, or
• when the children have been in the care of the third party for a period
Therefore, the courts in child custody disputes that involve third parties will, absent strong circumstances, keep the children or return the children to the custody of their own parents.
On the other hand, the court will be persuaded to give custody to a third party when looking at the circumstances involved it is presented with clear and convincing evidence that it is in the child’s best interests for the children to be given to that third person