.1 ohm but didn't notice any reading change or movement of terminal while taking the reading, I noticed the movement later and didn't take a reading then.
.1 ohm is pretty small for the average meter to be measuring. The test leads alone can offer that much resistance. What does the meter say when you short the lead tips?
The old analog meters had a zeroing function to make the meter read zero when the leads were shorted. I haven't seen a digital meter with that yet. But maybe there are some...
Anyway, that .1 ohms is not your problem, not in a smaller breaker. Those breakers have some resistance so that heat is generated in their bimetal components so that they will trip off at the engineered amperage. A low-amp breaker needs a bit more resistance than a 60-amp breaker does to generate the heat.
The loose terminal could be the problem. One of the terminals is one of the breaker's contacts, and the other it attached to the bimetal strip. Time to replace it. Loose stuff means intermittency.
Depending on the wiring and the type of regulator, that alternator field breaker handles very little current. It feeds the switch that connects to the S terminal on the regulator, and that terminal is only attached to the small coil on a small relay that turns the regulator on. The field current comes from the alternator output, or the bus, not the ALT breaker or switch. Like so:
An electronic regulator could need more current from the switch, such as in the common electronic regulators used by Cessna starting in the late '60s:
The "B" (battery) terminal is switched on by the switch, and the field current comes through it.
Some electromechanical regulators were wired more like the electronic ones, with the field power coming from the ALT switch. Piper:
Or Lake:
A 12-volt alternator's field will draw maybe 4 amps, so the breaker doesn't need to be big.