The correct expression is "a friend of mine," which is an idiomatic phrase in English. Step 1: Structure explanation
"A friend of mine" is a partitive construction, where "of mine" refers to someone who belongs to the group of people I call friends.
Why other options are incorrect:
- "off" is a misspelling in this context.
- "with mine" and "to mine" are grammatically incorrect and not used in such contexts.