Karo and Lietzmann’s Catenarum Graecarum Catalogus lists 28 different medieval Greek catenas on the psalms. These are not 28 different copies, but 28 different types. I confess that I have not yet read through all this material, and am awaiting the printed copy that I made and ordered.
Fortunately the printed editions of whatever exists appear at the front of each entry in K&L. This is meagre enough.
First there is a volume by the inevitable Balthasar Corderius, in three folio volumes: Expositio Patrum Graecorum in psalmos, a. Balthasare Corderio Soc. Iesu ex vetustissimis Sac. Caes. Maiestatis, & Sereniss. Bauariae Ducis mss. codicibus … concinnata; in Paraphrasin, Commentarium et Catenam digesta; Latinitate donata. & Annotationibus illustrata . . . Antverpiae, ex officina Plantiniana Balthasaris Moreti M. DC. XLIII- VI. 3 vol. fol.
This appeared at Antwerp in 1643-6 at the Plantin-Moretus press. I had not known that Corderius was a Jesuit, but so it appears. He printed his text from manuscripts belonging to the Emperor and the Duke of Bavaria. He also translated what he gathered into Latin.
The mss he used were Vienna 298 and 8 (possibly also Vienna 294 on Psalm 1-50). He also used Munich 12 and 13 to fill in what he considered to be gaps. The edition is plainly a collection of whatever Corderius thought useful, rather than based on an edition.
The second catena in printed form listed by K&L is this: Aurea in quinquaginta Davidicos Psalmos doctorum Graecorum catena. Interprete Daniele Barbaro electo Patriarcha Aquileiensi. cum privilegio. Venetijs, apud Georgium de Caballis. MDLXIX. fol. So this is earlier, 1569, in Venice. It looks as if it may only be a Latin translation. K&L give a list of authors and where the materials came from.
Most interesting of these to us are fragments of Eusebius of Caesarea’s Commentary on the Psalms. These are contained in this, and were edited by Montfaucon in his edition of that work. It looks as if he may have made use of manuscripts in Turin, which would be rather important as that manuscript was destroyed in 1904.