It depends on the context. It can be the preposition "με" (mainly equivalent to "with", though not restrictedly) or it can be the personal pronoun in either the genitive "μου" or the accusative "με" οf the singular.
This refers to -μ'- only.
The -'μ- you mention can be the idiomatic form of the possessive pronoun of the first singular person (my).
All the best,