There's . . . . . . . . small supermarket at . . . . . . . . end of . . . . . . . . street on which I live.

We are referring to a small supermarket in general. So, we need to use an indefinite article here. Since 'small' begins with a consonant sound, we should use 'a'.
'The' is used before specific or unique places/things. Here, 'end' is specific because there is only one end and 'street' is the specific one on which the speaker lives.