Science-based answers, please.
the main concern is radiation protection for sustainability of human life (and accompanying plant and animal life ecosystems, whether earth-like or not).
atmospheric retention is a minor concern (assume other factors have (mostly) taken care of the atmosphere, so it would only be a bonus if the parent planet's magnetosphere helps with this retention).
assume that similar atmospheric protections as are present on Earth (ozone, etc.) are also present on the moon, but that nothing extra exists on the moon itself to provide any additional radiation protection, and the moon has no magnetosphere of its own.
answers can assume a moon with any combination of factors within these ranges: mass ranging from .5 earth mass to 3 earth mass; diameter ranging from 3500 km to 14000 km; 75% earth gravity to 125% earth gravity
answers can assume a parent planet of any size/composition/configuration that current scientific understanding deems could plausibly exist, and that any layman could reasonably accurately label as a 'gas giant', regardless of accepted scientific definitions and terminology (including brown dwarf, ice giant, etc.) but that a layman would not even accidentally believe is a star or rocky planet.
answers can assume that radiation and stellar wind and any similar phenomena that are reaching the magnetosphere of the planet (and would otherwise reach the moon) from the star in this system is comparable to what Earths magnetosphere participates in defending humanity from, regardless of the actual size or type of star or the planet's or moon's distance from the star.
The research: The most relevant information I was able to find here are these questions which cover related and similar topics, but do not answer this specific question
The desired information:
Could a moon within the diameter/mass/gravity/etc. ranges mentioned above orbit any plausible 'gas giant' planet close enough to the planet to be protected by the planet's magnetosphere from the radiation and similar hazards created by the star without other adverse affects (roche limit, etc.)?
Is there any plausible composition of a celestial body that could be called a 'gas giant' and that could produce a large enough and strong enough magnetosphere to protect this orbiting moon, while not emitting or re-emitting so much radiation itself that it defeats this purpose?
bonus points for details on distances between moon and planet, orbital times, and similar considerations
This is my first question on stackexchange, so please be gentle, but don't hesitate to provide constructive criticism if I'm doing anything wrong.