If a standard C7 chord is made up of C,E,G,Bb, then your chord is only one note different, the root becomes C#. That is piece of cake for a piano player,- only one finger to move- and that is why the chord is such a common one in jazz.
I personally believe that the naming of any chord beyond a basic triad should be regarded as a mnemonic device at best.
According to context, you might be hearing that chord as C7flat9, C#dim, C#m7 etc etc.
The most common use for the chord is in the jazz version of the four chord turnaround that goes with songs like "Stormy Weather"
C C#dim Dm7 G7, quite a lot classier than C Am F G!
Cheers
Dave