I've often seen the word "Clerius" (Κληριος, "Klêrios") listed as an epithet of the Greek god Apollo, translated to "Distributing by Lot". I've searched a lot for the possible meanings of this phrase, but couldn't find a thing.
I think you'll find that it's Apollo Clarius (Klarios) that you're looking for. While both names occur on the site Theoi.com, only Clarius has an entry, which makes me think that Clerius may be a misspelling. That it turns up nothing on JSTOR and very few hits on Google seems to confirm this.)
Apollo Clarius was an Ionic deity, and appeared on coins from that area. He had a famous temple and oracle at Colophon, one of the 12 Ionic cities.
The Theoi.com entry for Apollo Clarius reads:
CLA′RIUS (Klarios), a surname of Apollo, derived from his celebrated temple at Claros in Asia Minor, which had been founded by Manto, the daughter of Teiresias, who, after the conquest of her native city of Thebes, was made over to the Delphic god, and was then sent into the country, where subsequently Colophon was built by the Ionians. (Paus. vii. 3. § 1, ix. 33. § 1; Tacit. Ann. ii. 54; Strab. xiv. p. 642; Virg. Aen. iii. 360; comp. Muller, Dor. ii. 2. § 7.) Clarius also occurs as a surname of Zeus, describing him as the god who distributes things by lot (klaros or klêros, Aeschyl. Suppl. 360). A hill near Tegea was sacred to Zeus under this name. (Paus. viii. 53. § 4.)