What is the group reagent for the zero group (ammonium cation) in inorganic salt analysis?
Ammonium salts are identified by the release of ammonia upon warming with base.
$$\ce{NH4+ + OH- -&gt;[\Delta] NH3 ^ + H2O}$$
Vogel's Qualitative Inorganic Analysis 5th ed., p 400 writes

6. Test for ammonium ions Boil a little (c. 0.1 g) of the substance with sodium hydroxide solution. The evolution of ammonia, detected by its odour and its action upon red litmus paper and upon filter paper soaked in mercury(I) nitrate solution,* indicates the presence of an ammonium salt.
* Drop-reaction paper, treated with tannic acid and silver nitrate solution, may also be used.