The correct order in aqueous medium of basic strength in case of methyl substituted amines is:

Order of basic strength of methyl substituted amines in aqueous medium.

Basicity in aqueous solution depends on both the inductive effect of methyl groups, which increases basicity, and steric or solvation effects, since bulky groups hinder solvation of the conjugate acid and thus lower basicity.

The experimentally observed order in aqueous medium is:

Me$$_2$$NH has a strong inductive effect and its conjugate acid is well solvated through two N-H bonds, MeNH$$_2$$ has a moderate inductive effect with good solvation, and although Me$$_3$$N has the strongest inductive effect, its conjugate acid is poorly solvated due to having only one N-H bond.

The correct answer is Option A: $$\boxed{\text{Me}_2\text{NH} > \text{MeNH}_2 > \text{Me}_3\text{N} > \text{NH}_3}$$.