Evolutionary Tree

[Esquilax]

Paternity tests do not use the same DNA sequences that phylogenetics use. The DNA sequence(s) that demonstrate paternity wouldn’t show any relationship to chimps.

A paternity test would not show paternity with a chimp, because a chimp is not paternally related to you, and that's sort of the point: what use would a paternity test even have if things that were not the father could still get positive results? If a chimp could get one, then so could any given human.

See, the trouble is that the question is malformed: while paternity tests do look only at specific sequences, the reason for this is that they're looking for completely different things, in this case duplicate sequences within the parent's DNA and the child's, while the full genome sequencing that shows a relationship between humans and primates look at the overall sequence for similarities. The basis for the former is that since DNA is derived from equal material from the two parents, a given child should have specific identical sequences with either parent. The basis for the latter is that overall similarity between two given complete genomes shows an ancestral relationship between the two species, since every observation we have bears this out.

So yes, a paternity test would not establish a relationship to chimps, which is trivial, because your parent was not a chimp. Using this as evidence against evolution, though- and I know it's not you doing this, Roadrunner- would be roughly akin to saying that fridges don't work because you can't cook a turkey dinner in one. It's asking the tool to do something it's completely unfit to do.