It's hard to believe that there were ever questions about the authenticity of this sonata, but one of the earliest doubters was Haydn himself. In conversations with Griesinger in 1803, Haydn first confirmed and then denied his authorship of this work. Even earlier, in a 1790 edition by London publisher Cooper the work had been attributed to Haydn's student Ignaz Pleyel. However, the sonata appears in the Breitkopf catalogues of 1763 and 1767 as being by Haydn — which removes Pleyel from consideration (he was born in 1757, nor was he any kind of Mozartean child prodigy.)
The sonata has never been absent from editions of Haydn's piano sonatas; there's no reason to doubt its authenticity. In fact, I find it very difficult to imagine it being by anyone else. It demonstrates a number of features that were very much part of Haydn's language in the late 1750s. The first movement in particular shows strong connections with the Mannheim school, influences which also pop up in Haydn's first symphony of 1757. Among those traits are the "Mannheim crescendo", which appears to be the inspiration for measures 7 - 10 as an orchestral technique is transferred to a keyboard instrument. (At least that's the way I perform it.)
Even more telling, to my mind, is the figure in measure 11, which is gloriously and ubiquitously Haydn: throughout his career, Haydn exulted in taking cross-relations right to the edge of tolerance, almost like a little boy who loves to play with matches and has become so skilled he is certain he can do almost anything without burning the house down. This is the first instance I know of one of Haydn's "cross-relation dares" in the piano sonatas:
In fact, the cross-relation helped me to interpret the passage: by emphasizing the A-A#-B motion in the bass, the cross-relation is kept safely at bay.
First Movement: Moderato
The very opening of the movement is possibly another Mannheim idiom: the coup d'archet, or strong stroke of the bow on the strings of the violin. I was quite intrigued by the notation of the opening chord, a polyphonically stemmed arpeggiation:
I'm interpreting the unusual notation as pointing towards some kind of special effect, which I have performed as a swift, on-the-beat upwards arpeggio in an attempt to mimic the sound of a Mannheim coup d'archet.
The movement remains firmly in a 1750s style given that there is no clear distinction between secondary and closing themes: a single B Major theme does yeoman's duty for both.
I should also mention that the movement presents us with another Haydn 'handprint' that was to show up with dependable regularity beginning in the 1770s: the premature recapitulation, or a recapitulation that is in the correct key, but far too early in the development to be heard truly as a reprise.
Second Movement: Menuet
Galanterie prevails in this delicate movement, while a minor-mode Trio provides a bit of darkness. Given the prevalence of irregular phrase lengths during this era, it's worth noticing that most of the phrases are square-up four-measure affairs, save two short expansions in the final phrases of both the minuet and Trio.
Third Movement: Finale - Presto
If I needed any more evidence of this being 100% Haydn (although I don't), this movement would clinch the deal. It's a great example of a "Haydn Looney-Tunes" movement — an insanely fast duple meter affair that sounds for all the world like the Coyote and Road-Runner streaking across the Arizona highways. Because this little frolic tends to show up in intermediate-level piano anthologies, we've all become rather drearily accustomed to hearing it played dutifully or unimaginatively. However, taking it at a recklessly frenetic clip without the slightest hint of raised-pinky gentility reveals it as the wacky little gallop that it is, an early example of one of the longest running jokes in music history.