Akhilles was the son of sea-born Thetys and Peleus. He was the prince of the Myrmidons of Phthia. According to later tradition, he was dipped into the River Styx, but his ankle was left vulnerable. He was recognized as one of the best fighters of the Achaeans next to Diomediz and was known as the Aristos Achaion – Best of the Achaeans.

Patroklus was the son of Menoetios and Philomela – though sources vary on who his mother was. He was the prince of Opus, but exiled and taken under Peleus' wing after killing a fellow prince over a game of dice. He was a suitor of Helena and was bound to the oath of Tyndareos. He was Akhilles' closest companion, whether it was brotherly or romantic is up to you. He fought with the Myrmidons during the Trojan war, before being killed by Hektor of Troy in Book 16.

The two spent their boyhood with Kheiron, the centaur and son of Kronus. They were educated and trained on Mount Pelion together. Although this seems to be a later tradition, seeing as it is only mentioned by the Roman poet Statius in the Achilleid.

After the death of Patroklus, Achilles asks for his own ashes to be mixed with his comrade's, so they could be inseparable even in death.

Hero cult and Historical Worship.

According to J. T. Hooker, the cult of Akhilles seems to have been widespread, from Aeolis to the shores of the Black Sea. While the two were buried together, the cult is commonly referred to as the 'Cult of Achilles'. This seems to have been a cult of the dead.

But at this point Hommel inserts into the argument some literary allusions, which tend (in his opinion) to prove that Achilles was regarded as the lord of Leuce, the original centre of the cult. From this fact Hommel draws the further conclusion that, long before Achilles was incorporated into heroic saga, he received divine honours as the lord of the dead souls beyond the sea; and, according to Hommel, Achilles' status as lord of the dead is reflected in the Odyssey.

— THE CULTS OF ACHILLES by J. T. Hooker, page 2.

Unfortunately, most of the details of this cult are obscure. We do know such a cult existed thanks to accounts of Alexander the Great's visit and him paying respect to them.

Modern worship.

Taking source from user hero-shrine (please do look at their blog! I couldn't see their post on Patroklus sadly.)

Akhilles seems to be commonly associated with feelings of rage and bloodlust, but some associate him with homosexuality. Patroklus seems to be associated with war and glory, but has associations with medicine (UPG!), companionship and loyalty.

Symbols of Akhilles are commonly the lion, the spear, the shield, and the lyre. Patroklos has similar to same symbols, but with the addition of hounds.

Epithets of Akhilles are: Son Of Peleus/Peleides, Aristo Achaion (Best of the Achaeans), Lion-hearted.

Epithets of Patroklus are: Son of Menoetios/Menoetides, Gentle-hearted, Kind-hearted, Of Heavenly Birth*. *NOTE: as Reddit user u/LucySofer pointed out, Patroklus seems to be 'unworthy' of this epithet as he is not descended from a god. User u/elsharra has suggested this could be a compliment in the same sense of 'like a Saint'.

Offerings to them can be the usual offerings you'd give gods and spirits. Honey, wine, bread, flowers, incense or anything that smells nice. Poems, artwork, and a playlist also suffice. If you will make an altar for either of the two or together, please do not put them next to a deity they have bad blood with! Learn their myths before you do.

Devotional acts to Akhilles can be: learning the lyre or learning an instrument, picking trash from the beach or sea, telling your loved ones that you love them, giving your loved ones gifts, ethically collecting seashells, learning a sport, reading about his myths, read the Iliad.

Devotional acts to Patroklus can be: learning medicine, herbology, or the medical properties of plants, taking care of dogs, standing up to your loved ones, giving your loved ones gifts, learning a sport, reading his myths, read the Iliad.