How to tune GPS Antenna with a PI circuit and spectrum analyzer?
An antenna that is not correctly tuned will degrade your input signal. Ie you will get lower signal levels and less SNR. This will degrade your position solution, but not consistently so. Ie if you have a consistent offset in your position, this is more likely due to reflections (aka multipath) of buildings/trees/objects in the vicinity and not due to your antenna. Multipath is worse with chip antennas than with patch antennas as the latter are circular polarized antennas, that dampen reflected signals to some extend, while the former are linear polarized antennas that accept direct and reflected signals with the same strength.

The book "GPS/GNSS Antennas" by Rao explains the effects and how to deal with them in details.

Though, you are saying that you are 0.1degree off, which is roughly 8km. That is a lot, even for multipath (that usually causes a few dozen meters to a few 100m). It is more likely that your GPS receiver has problems, either with the signal levels or a genuine firmware bug.