  We present a RR Lyrae (RRL) catalogue based on the combination of the third
data release of the Zwicky Transient Facility (ZTF DR3) and \textit{Gaia} EDR3.
We use a multi-step classification pipeline relying on the Fourier
decomposition fitting to the multi-band ZTF light curves and random forest
classification. The resulting catalogue contains 71,755 RRLs with period and
light curve parameter measurements and has completeness of 0.92 and purity of
0.92 with respect to the SOS \textit{Gaia} DR2 RRLs. The catalogue covers the
Northern sky with declination $\geq -28^\circ$, its completeness is $\gtrsim
0.8$ for heliocentric distance $\leq 80$~kpc, and the most distant RRL at
132~kpc. Compared with several other RRL catalogues covering the Northern sky,
our catalogue has more RRLs around the Galactic halo and is more complete at
low Galactic latitude areas. Analysing the spatial distribution of RRL in the
catalogue reveals the previously known major over-densities of the Galactic
halo, such as the Virgo over-density and the Hercules-Aquila Cloud, with some
evidence of an association between the two. We also analyse the Oosterhoff
fraction differences throughout the halo, comparing it with the density
distribution, finding increasing Oosterhoff I fraction at the elliptical radii
between 16 and 32 kpc and some evidence of different Oosterhoff fractions
across various halo substructures.
