The farthest you can see in the sky with your telescope will depend on its ability to gather light and where you observe.
The most distant objects visible with amateur-sized telescopes are faint galaxies and the brightest quasars. They will be brighter and easier to see in a telescope that gathers more light and has a greater magnitude limit. Here bigger is better and a larger aperture scope will see more remote objects.
Location is also important. Even with a big telescope, you’ll see fainter, deeper and farther out into the universe from an isolated dark-sky site than from the heart of a megalopolis. For example: quasars are all very faint as seen from the earth. The brightest one is 3C 273 in Virgo. It is magnitude 12.9. A good 4-inch scope is capable of seeing it in dark-sky conditions. You’ll need a larger scope to be able to see it at all from a city.