Did Sirius Black want to kill Harry Potter?

It was because of the prophecy that Professor Trelawny had made that said that both could not live

Specifically, all Voldemort finds out of the prophecy is that the one named in the prophecy would have the power to defeat him. He does not find out about the second half, that effectively seals his fate, that neither can live while the other survives or that he will mark that one his equal.