Yet even as the rest of his species vanished into obscurity Apollo never gave up on the hope that humanity would some day spread to the stars and planned on restoring the "natural order" by turning humans back into worshippers whilst he would serve as the father of a new generation of "gods" - despite Apollo likely feeling his plan was honorable the humans of Kirk's era had no interest in becoming the servants of another species and thus Apollo clashed with the Starfleet officers.
Who Mourns For Adonis?
Investigating a power source emanating near a planet, Kirk and company found their ship in the grip - seemingly the literal grip - of a powerful force that would not let them depart. A Human-looking being appeared on the viewscreen, calling himself Apollo, and that he was in fact the Apollo of Greek myth. He demands a landing party descend, taking care to exclude Spock, who reminds him of the trickster/satyr Pan, apparently someone he didn't get along with. Seeking to free his ship, Kirk acquiesces, taking Doctor McCoy, Lieutenant Commander Scott, Ensign Chekov and Lieutenant Carolyn Palamas, an expert on Earth's history and a devotee of the myths of ancient Greece and Rome. Upon beaming down, the crewmembers learn that Apollo and his kind were alien visitors to ancient Earth, coming from other worlds and aiding in the building of Earth's great civilzations. Their innate powers and technology saw their worship as deities, which Apollo plans to oversee the resumption of. His designs on Palamas enrage Scotty, while his threats against the Enterprise and his crew enrage Kirk. For his part, Apollo is confused and angered by the crew's outright rejection of his paternalistic plan for Humanity, in his vision reduced once more to an agrarian society cared for by the gods of old. Showing that his power is no myth, Apollo is able to manipulate vast fields of energy, continue to threaten the ship, and command the weather to punish and chastise what he sees as wayward children. With information on Apollo's physiology and the apparent source of his power, Kirk gambles their lives by having Enterprise conduct an all-out attack on Apollo's temple-structure, which contains a complex device to enable his personal energy/matter manipulation. When the temple is destroyed, Kirk makes it clear again, that, while they are grateful for what Apollo's people did for them in the ancient past, that time is gone, and Humans have moved on. Apollo reluctantly accepts his fate and moves on to the plane of existence his fellows left for ages ago. Kirk expresses a minor regret for having lost someone who once gave them so much.
Apollo's attacks during this included hitting the men with lightning, partially stripping and 'ravaging' Palamas with wind (ancient gods were said to use elemental and animal forms to achieve difficult seductions) and bombarding the Enterprise while having an energy-field vice-grip on its hull. His scheme, if enacted, would have casually undone centuries if not millennia of Human progress. While very well-intentioned, his understanding of Humans was vastly out of date. In this lack of understanding, he is similar to the childish Trelane, while his echoing cry while fading was reminiscent of Charlie Evans.
Powers / Abilities
Apollo claimed to be an Ancient Greek god (Olympian) but he was not an actual deity, instead he was an advanced alien life-form who displayed godlike powers (in a similar fashion to the Q, who would be discovered many years after Apollo).
Apollo's powers were sufficient though that pre-Warp societies would of almost universally of seen him as a supernatural being and even Warp-capable societies such as the Federation found him to be a formidable opponent.
Amongst the least of Apollo's known abilities are electrokinesis (which he manifested via firing beams of lightning), ergokinesis (the creation of an elaborate force-field that mimicked a giant human hand) plus size-alteration (able to grow to gigantic size without apparent harm to himself).