Is there any other solar system in this Milky Way Galaxy?

Let's compare definitions here astronomically.  A solar
system is a set of planetary bodies orbiting a star.  A galaxy is a massive collection
of stars.  The Milky Way is the name for the galaxy in which our solar system
resides.

So the answer to your question is not only yes,
but repeatedly yes.  Hundreds, thousands, even tens of thousands of solar systems exist
within our galaxy, and within every galaxy in the
universe.

The Hubble Space Telescope has already identified
more than 400 planets outside of our solar system within the Milky Way Galaxy, including
some which appear to have atmospheres and water or ice.