Here's how your Telecaster
should sound
:
https://www.youtube.com/watch?v=yO2CcGgIeOs
No distortion, no overdrive (or very little). Instead, a fair dose of
reverb - partly from the amp, partly from the venue.
Here's more "Jazz Tele":
https://www.youtube.com/watch?v=zDuee6blvj8
(There's a touch of chorus effect there, as well as reverb.)
Again, as the others say, check your amp settings. If there is a "master" volume, there will be another labelled "gain" or just "volume" - keep the latter one low (not off, just very low), and use the master to get it as loud as you want. You could also keep your guitar volume knob down a little (not on full).
Of course, if your amp has a "clean" channel (or "rhythm" as opposed to "lead") use that. "Lead" or "dirty" channels are designed to have some distortion applied. (Sometimes the "gain" control will only affect that channel.)
You'll also find your neck pickup has a mellower sound than the bridge pickup. Both should be "clean", but the bridge pickup has a brighter tone which some ears may find harsh. If you can have both PUs on, that gives you the broadest tone spectrum.
Naturally, you can fiddle with the tone controls too - on both guitar and amp.