Can a city supersede a state law if unspecified?

Living in Indianapolis i can tell you that state law will triumph any city law.

Indianapolis according to state law in Indiana is a class 1 city and the only one in the state. As a result of the Unigov law passed by Mayor Richard Lugar and the Indiana General Assembly in 1969 Indianapolis gets special treatment in regards to laws passed for cities. The Indiana General Assembly can pass laws that restrict what Indy does. This is both good and bad. For example Democrats on the city council have been stalling progress in the city to try and score political points against the Mayor and as a result the Indiana General Assembly removed the 4 at large seats on the council which are all held by Democrats.

Another example might be in the future if Democrats get full control of the city and the council they might pass a minimum wage bill of 10-15$ an hour. Even if they do that the Indiana General Assembly can pass a law nullifying that law in Indy. so the Indiana General Assembly keeps the city in check.

Generally speaking, if something isn't specified at a "higher" level, a "lower" level can put in its own laws.

If there is no state law on an issue, it's not possible for a city to "supersede" it. There's nothing there in the first place to supersede. The city should be able to do what it wants.