about "꺼" The original form is "것", but '거" is more common in spoken language. "꺼" is the pronunciation of "거", so it's a spelling mistake. "것" is a bound noun which needs the complement. --> 내(the contraction of 나의) 것 (mostly in written language) - 내 것 --> 내 거 (in spoken language - sounds as 내꺼)

A little context would help, but 의 is a possessive marker in Korean, such as the " ' " in my older brother's car / 형의 차 and the only relation I see between 의 and 꺼 is that 나의 것 can be contracted to 내꺼 (my thing/stuff/item)