Learn Icelandic: Ég hitti sambekkinginn minn í gær.

It attaches to the stem of bekkur (class) and takes the suffix -ingur (used to indicate a person). Together, sam- (co- or shared) plus bekk- plus -ingur literally creates a co-class-person, meaning classmate.

Why is the definite article used in sambekkinginn minn if the English translation just says my classmate?

In Icelandic, when a possessive pronoun like minn comes after the noun, that noun almost always takes the attached definite article. You are literally saying the classmate my, which is the standard everyday way to express possession.

Why does the word end in -inn instead of -urinn?

The verb hitta (to meet) requires its direct object to be in the accusative case. The nominative masculine form is sambekkingurinn, but in the accusative, the -ur ending drops, leaving sambekkinginn. The pronoun minn is also in the accusative here, though it happens to look identical to its nominative form.

Is the sam- prefix used with other suffixes to mean a co-person?