The concept of being part of another galaxy's solar system is an intriguing idea, but based on our current understanding of galaxies and solar systems, it is highly unlikely. Let me explain why.
A solar system, like our own, consists of a star (in our case, the Sun) and the celestial bodies that orbit it, such as planets, moons, asteroids, and comets. These objects are gravitationally bound to the star and form a cohesive system.
Galaxies, on the other hand, are vast collections of stars, gas, dust, and other celestial objects held together by gravitational forces. The size and scale of galaxies are much larger than solar systems. Our Milky Way galaxy, for example, contains billions of stars, and each star within it has the potential to host its own solar system.
The distances between stars within a galaxy are immense, even though the stars themselves are relatively close compared to the size of the galaxy. The vast majority of stars in a galaxy are not physically close enough to each other to form a shared solar system. The distances between stars are typically measured in light-years, which is the distance light travels in one year (about 9.46 trillion kilometers or 5.88 trillion miles).
Considering the immense distances between stars, it is highly unlikely that we are part of another galaxy's solar system. Our solar system is within the Milky Way galaxy, and the Sun is located in one of its spiral arms. The gravitational influence of the other stars in the Milky Way is generally negligible on the scales relevant to our solar system.
It's worth noting that galaxies can interact and collide, as I mentioned earlier. During such interactions, stars can be gravitationally disrupted or transferred between galaxies. However, the chances of a star from another galaxy becoming a part of our solar system are incredibly low due to the vast distances involved.
Therefore, based on our current understanding, it is most reasonable to assume that our solar system belongs to the Milky Way galaxy rather than being part of another galaxy's solar system.