This painting is one of three the artist painted of his mother.
The artist painted three paintings of his mother. This painting is one of them.
This painting is one of only three the artist painted of his
mother.
The artist painted only three paintings of his mother. (The speaker thinks three paintings of his mother is a small number of paintings, small enough to be mentioned as a fact in its own right.) This painting is one of them.
This painting is one of the three the artist painted of his
mother.
The artist painted three paintings of his mother. (The speaker is referring to that trio of paintings as if the listener is already aware there was a trio of paintings, or to introduce the fact that there was a trio, possibly because the speaker intends to discuss all three.) This painting is one of them.
This painting is one of the only three the artist painted of his
mother.
Same as immediately above, in terms of the assumption that the listener is aware of the three, or to introduce the fact that there were three, coupled with the idea that three is a small number.
P.S. This last version, "one of the only three", strikes my ear as odd, but it is well attested.