this is sort of like a stray horse in a paddock with the other horses in the pen next door... and it will be easier to bring all the other horses in to that paddock so they are now all together... rather than chase that C# round in circles all day.
C# is a tricky one because it is only the air going through the horn as there are no fingers being held down... which would increase the length of the 'saxophone tube'...
think about ways to work on that C# by incorporating it into something else... practising that particular note in relation to other things will 'increase the depth of your sounding of the note'... or... the timbre...
so... C# (hold that note if it is your emphasis)... these all have that 'C#' in them whilst avoiding the palm keys a little bit.
C#major arpeggio C# - F - G# - C#
C#minor arpeggio C# - E - G# - C#
D major 7 chord D - F# - A - C#
Eb dominant chord Eb - G - Bb - Db/C#
E major 6 chord E - G# - B - C#
F augmented triad F - A - C#
F#minor triad F# - A - C#
F# major triad... F# - A# - C#
A major triad A - C# - E
Bb minor triad Bb - Db - F
also... start on the C# and go down chromatically returning to the C# using that as a pivot note... C#-C-C#, C#-B-C#... the link below... you can do that up the octave... and even do that exercise all the way up to top f with the three palm keys and side e key.
http://www.tristanhallmusic.com/tristanwebsite/Educational_files/lownotes.pdf
there is a lot of different ways you can approach one particular note that will bring it back on par with the other notes... every now and again you can clean the hole on the neck with ? an ear bud cleaner thingy incase it is blocked...(my problem at the moment)..