The UKIRT M33 Monitoring Project - VII. A 15-year K-band photometric catalogue of long-period variable stars in the central kiloparsec of M33

We present a homogenised K-band photometric catalogue for the central ${\approx}12$ arcmin$^2$ (${\approx}0.9$ kpc$^2$) of the Triangulum spiral galaxy M33, combining four independent PSF-based near-infrared datasets obtained with UKIRT between 2003 and 2018. These comprise the 2003-2007 UIST multi-epoch monitoring survey, the 2005 UFTI K-band mosaic (for which we present new PSF photometry), new WFCAM PSF reductions for the four central tiles, and a single K-band epoch from the 2018 UKIRT Hemisphere Survey (UHS DR3). Cross-matching all four catalogues and retaining stars detected in at least two of them yields 847 unique stars comprising 21,085 valid K-band measurements spanning a baseline of 15.11 yr. Photometric homogenisation onto the 2MASS/Vega system via 82 low-scatter calibration stars removes systematic inter-dataset offsets of up to 0.22 mag. Of the 847 monitored stars, 771 (91 per cent) are classified as variable ($σ_{\rm rms} > 0.10$ mag), including 385 high-amplitude variables ($A_K \geq 1.0$ mag): prime Mira-type long-period variable candidates for period determination. Cross-matching with archival Spitzer IRAC photometry yields 156 matched stars, of which 120 satisfy $\langle K\rangle - [3.6] > 0.5$ mag, identifying dust-enshrouded AGB candidates inaccessible to all-sky optical surveys. This catalogue constitutes the most extensive near-infrared photometric baseline assembled for AGB stars in any spiral galaxy beyond the Milky Way, providing the photometric foundation for the period-luminosity analysis and star-formation-history reconstruction in the companion Paper VIII. The full catalogue is available at the Centre de Données astronomiques de Strasbourg (CDS).