Quake3World

I always get this (I guess it's an error) while trying to play online.

I get the message "Awaiting Gamestate... 1... 2... etc.," and about 75% of the time this message will appear:

"This server uses protocol X" (it usually says 63 or 48)

How can I fix this error?

means youre using a different version of quake3 than the server
grab the latest point release (1.32c) and install that, that will fix it

1.16 43
1.17 45
1.2x 48
1.30 66
1.31 67
1.32 68

above is the point releases and protocols, as you can see there is no protocol 63.
make sure you write down/take note of which protocol the server you are connecting to says it is using and use the above list to find the correct point release you need.