Does this pushdown automaton describe the language {$a^n b^n c^i \in \{a,b,c\}^*\ |\ n \ge 0,i\ge 0$}?
As I am (not) yet certain of the PDA model you are using, I will not comment on correctness of your construction, but I have a general remark on PDA.

There happen to be two generic ways of defining languages for PDA: by final state and by empty stack. Let a configuration be a description of the PDA, its (yet unprocessed) tape, state, stack.

Using final state acceptance means that we accept any word that leads from the initial configuration of the automaton to a configuration that is in a final state (no matter what is the contents of the stack) after reading the complete input.
Similarly, empty stack acceptance means that we accept any word that leads from the initial configuration of the automaton to a configuration in which the stack is empty (no matter what is the state) after reading the complete input.

By standard constructions one is able to change a PDA into an equivalent one using the other acceptance type. so for practical reasons the two notions are interchangeable. When dealing with technicalities (in case of deterministic automata for instance) the acceptance type does matter.

In conclusion: if you are using final state acceptance, then do not worry about remaining stack symbols.