inner city, inter-city

Inner city or inner city most commonly means blighted or impoverished parts of a city--
Abandoned properties are a serious problem for inner city neighborhoods.
The mayor should ask the council to vote for increased funding for the inner city.

Inter-city or inter-city describes something that takes place between two or more cities--
There is an inter-city bus line that will get you there in about an hour.
The annual football game is part of a long history of inter-city rivalry.

Now that you know that, you can say--
"Young people from the inner city will participate in an inter-city competition."