With the given production rule:

A$->$AA$->$A

This production rule specifies that the nonterminal symbol AA can be replaced by itself. However, there are no terminal symbols $(0$ or $1)$ in the production rule, and there are no other production rules. As a result, there is no way to derive any string containing terminal symbols from this grammar.

In context$-$free grammars, the language generated by a grammar is the set of all strings of terminal symbols that can be derived from the start symbol. In this case, since there are no terminal symbols in the production rule and no way to derive any, the language generated by G$0$ is the empty set $($denoted by $).$

So$,$ it is correct to say that G$0$ generates the empty set. The grammar is essentially not generating any strings with terminal symbols.