Hi, I'm not sure why it's important for these chords to be exactly three strings, but here's a few common three string chords that I use in jazz reasonably often:

--------------------------------------------------------
--------------------------------------------------------
----5-----------6------------5--------------------------
----4-----------4------------3--------------------------
----5-----------5------------5--------------------------
--------------------------------------------------------

The first is D7, the second is Dmajor7, and the third is Dminor7. Bear in mind that these chords are all missing the 5th.
To make them into 4 note chords, I would usually play this:

--------------------------------------------------------
----5-----------5------------5--------------------------
----5-----------6------------5--------------------------
----4-----------4------------3--------------------------
----5-----------5------------5--------------------------
--------------------------------------------------------

D9, Dmajor9, Dminor9

I'm sure I haven't answered your question properly, but those chords are good to learn anyway, I use them every day!