The Quadrantids (QUA) begin in late December and peak on the night of 3rd/4th January. The best time to view will be after 5am when the nearly full Moon sets and the radiant will be high in the East. After moonset, rates of up to 20 an hour are possible.
There are no other significant showers till April, but the IMO reports that there’s a possibility of an outburst of the minor shower k-Cancrids on the 10th of January at 04h UT. If you pick this up, please let us know as more data are required. Meteors will be relatively fast moving and the radiant is below the waning crescent Moon.
For southern hemisphere observers there’s also the possibility of a meteor shower due to an encounter with debris from minor planet 2016BA14, on 23rd March between 00h and 04h UT. The radiant, in Pictor, is well below the horizon for northern hemisphere viewers but there’s no Moon at this time, so do watch out for slow-moving meteors appearing to move upwards from the horizon.