Mysterious Intonation issues :(

[Roseweave]

I got a new Xaviere Tele recently and the intonation is way out of whack on the 3rd fret of the E string. My old 7 string had the same problem so this is just FFF. While I think the 7 string was down to the nut, this is entirely mysterious. It's off by 20 cents almost, so there'd have to be a major notable deviation in the frets for it to be the frets, adjusting the nut does nothing(lifting the string up on the nut, putting paper underneath it etc.) and neither does the intonation. It could be the neck/truss rod, but the A string is more or less fine.

What could it be? Maybe the strings? that's about all I can think of now. I didn't want to change them as i like how they sound, but it's entirely possible I got a duff E string.

[sev]

The only thing I can think of is...are you squeezing too hard when you fret?
(Either on the 3rd fret, or at the 12th while intonating)
If your frets are on the large/high side, it's way easy to bend out of tune if you apply too much pressure.

[metalmariachi]

could be nut slot hight, or even a high fret.

Fuzzy may well be right, try resetting the intonation exactly on the fret rather than behind it

MM