It's likely to be a torpedo boat or destroyer. I did a quick survey of Fighting Ships Of The World..
Note that there is the speed achieved on trials, and the "name plate speed" guaranteed by the builders. Trials are often messed with to achieve higher numbers. For example, Forban reached 31 knots in trials being the first vessel to do so, but had a name plate speed of 29 knots. For this reason I've used name plate speed.
The fastest I could find is a single German torpedo boat of the S138 class. V161 was completed with 2 turbines and 4 coal boilers and could achieve 32 knots. Prior ships of the class used slower vertical triple expansion steam engines. Later ships would use mixed coal and oil boilers (see below).
The British built many "30-knot destroyers", coal fired with triple expansion steam engines rather than turbines. Several were "builder's specials" modified to attempt 33 knots. They did not succeed. HMS Albatros made 31.4 knots HMS Express, 31 knots, and HMS Arab 30.7 knots.
Many of these 30-knot destroyers were built for other navies. Ikazuchi, Akatsuki, and Shirakumo classes made 31 knots in Japanese service.
Mixed coal and oil
For this section, I'm counting ships which carry more coal than oil. This discounts, for example, the Amatsukaze/Isokaze class which could do 34 knots but carried more oil than coal.
Multiple classes could make 32 knots. They all used steam turbines.
- Austro-Hungarian made Tátra-class destroyers had 4 oil and 2 coal boilers producing 15,400 kW.
- Japanese Enoki-class destroyers had 4 boilers which could take coal or oil.
- French Aventurier-class destroyers used 5 mixed-firing boilers to produce 13,000 kW.
- British Faulknor-class flotilla leaders used 6 boilers to produce 22,000 kW.
- Many German large torpedo boats used turbines with a mixed of coal and oil boilers: G169 group, S165 group, S176 group, V180 group, G192 group, V1 class, G7 class, S13.