I have not got no money on me.

Any - this is the right option because the quantifiers 'some' and 'any' are used with plural and uncountable nouns, as in when we discuss an unknown amount or number of objects. For negative sentences, use 'any'. Because the statement implies that the speaker is poor.
Some - This answer is wrong since the noun 'money' in theis uncountable. The quantifiers 'some' and 'any' cannot be used interchangeably. In affirmative statements, the word 'some' is used. Because the statement implies that the speaker is poor.
None This option is incorrect because None' is the pronoun form of 'no'. It is used to replace countable and uncountable nouns, but it is never used directly before the noun. In the statement the noun is 'money'.
No change - This is incorrect because No' is used in a sentence to express that something doesn't exist, but if there is another clause that makes the sentence negative, we should use 'any' instead of 'no'.