Could a gas giant orbit a star with a 30 year period at a distance of just 1 AU? Assuming a star with similar properties to our sun, could a gas giant orbit it with an orbital period similar to that of Saturn, but, at a much closer orbital distance, more similar to 1 AU?
Gas giants can be found very close to their suns. The closest ones are then called Hot Jupiters.
But not with a orbital period of 30 years. Everything that orbits a star with one solar mass at 1 AU will also have an orbital period of 1 year, according to Keplers 3rd law:
$$
T^{2}=\frac{4 \pi^{2}}{G M} a^{3}.
$$