As pointed out in comments, there is a detailed survey by Tits from the algebraic group viewpoint in his AMS proceedings paper, along with quite a few references to earlier literature. From the viewpoint of groups over local fields, it's worth looking closely at his table of "indices" at the end of the paper. There he shows concisely which labelled Dyhkin diagrams can occur over various kinds of fields. In particular, you are interested in the twisted type $^2 \! A_n$ with $n$ even. He indicates that in the local field case this diagram can occur only relative to a quadratic extension and corresponds then to a quasi-split special unitary group. In his set-up, "quasi-split" corresponds to the case where $n$ is twice the relative rank $r$ and the Dynkin diagram is folded accordingly. (In general, various special unitary groups over division algebras are possible.)
While Tits does not spell out all the details of how such groups are constructed, he does provide a nice overview of the basic algebraic group theory leading to such a classification list. (Some improvements are contained in his 1971 paper Représentations linéaires irréductibles d'un groupe réductif sur un corps quelconque (MR).) Also, student of his at Bonn named Martin Selbach elaborated further on the theory:
Klassifikationstheorie halbeinfacher algebraischer Gruppen.
Diplomarbeit, Univ. Bonn, Bonn, 1973.
Bonner Mathematische Schriften, Nr. 83.
Mathematisches Institut der Universitat Bonn, Bonn, 1976. v+140 pp.
P.S. For the characteristic 0 theory, presented in a different style, you might try the lecture notes by I. Satake (which I haven't looked at in a long time): Classification theory of semi-simple algebraic groups. With an appendix by M. Sugiura. Notes prepared by Doris Schattschneider. Lecture Notes in Pure and Applied Mathematics, 3. Marcel Dekker, Inc., New York, 1971. viii+149. Satake also used labelled Dynkin diagrams, but with different conventions than Tits ("Satake-Tits diagrams").