‘Мой коллега’ or ‘моя коллега’?

In fact, both forms are correct, because the word ‘коллега’ is a sort of a hermaphrodite. That means that the word can be masculine or feminine, depending on the gender of a colleague we are referring to. See for yourself:

• Мой коллега Игорь всегда опаздывает. = My colleague Igor is always late.
• Моя коллега Ирина всегда опаздывает. = My colleague Irina is always late.

‘Игорь’ is a male name and ‘Ирина’ is a female one.

Such ‘hermaphrodite’ words are called common gender nouns. They normally end in -а or -я, but their gender (masculine or feminine) can be defined only in a context. The gender of adjectives and of possessive pronouns will respectively depend on the gender of a person being called by this common gender noun.

In the next publication we will see more Russian common gender nouns and will discover their meanings.