In German, 'mein' is the correct possessive article here. 'Das ist mein Handy' means 'This is my mobile phone'. Since 'Handy' is the direct object (accusative case) and is a neuter noun, 'mein' (nominative/accusative neuter) is correct. 'Meinem' is dative, 'meiner' is genitive/feminine dative, and 'mines' is not a German word.