Myths

[Janel]

Hero of the Trojan war------cousin of Achilles

[cancross]

Ajax

[sullimonkey]

Patriculus, although he was known as his best friend/lover,
thats why achilles was distraught when he was killed and took revenge on Hector the Trojan Prince. Hope that was what you wanted to know x

[Lysistrata]

Ajax was definitely Achilles' cousin (son of Telamon), but I'm now confused re Patroclus. I had a vague idea he was sometimes referred to as a cousin, but this doesn't seem to be supported by any account of his genealogy - at most he is actually, bizarrely, Achilles' nephew by a much older half-sister.
Homer doesn't mention this though. In the Iliad he's no relation, but the son of Menoetius and Achilles' older companion/mentor; both were taught by Chiron. It's in Iliad book 11.

[aredeegee]

Patroculus and Ajax are both cousins of Achilles. Patroculus was his lover, too. P's death in A's armour led to A killing Hector and treating his body appallingly until begged for its return by Priam, king of Troy and H's dad.