[Grammar] in/on the third day

[marker]

Which sentences are correct?

In the third day, we went to a museum.
On the third day, we went to a museum.
The third day, we went to a museum.
Third day, we went to a museum.

And what about sentences with 'next'? Do the same rules apply?

In the next day, we went to a museum.
On the next day, we went to a museum.
The next day,we went to a museum.
Next day, we went to a museum.

Thanks in advance for replies .

 

[5jj]

On the third day, we went to a museum.
The third day, we went to a museum.

On the next day, we went to a museum.
The next day,we went to a museum.
Next day, we went to a museum.

Those are possible.