John 20:1 Now on the first day of the week cometh Mary Magdalene early, while it was yet dark, unto the tomb, and seeth the stone taken away from the tomb. (ASV)
We see here that Jesus rose on the first day of the week, which is one of the reasons why we worship on the first day of the week. It is a celebration of His resurrection.
Acts 20:7 And upon the first day of the week, when we were gathered together to break bread, Paul discoursed with them, intending to depart on the morrow; and prolonged his speech until midnight. (ASV)
We have here a Apostolic example where the church met on the first day of the week to break bread (Lord's Supper) and for a discourse, aka sermon.
I haven't seen anywhere that we are commanded to meet specifically on any particular day, but I do see our tradition of doing so.
I also see guidance in making sure that we continue to assemble.
Hebrews 10:24-25 and let us consider one another to provoke unto love and good works; not forsaking our own assembling together, as the custom of some is, but exhorting one another; and so much the more, as ye see the day drawing nigh. (ASV)