This paper contains several methods for estimating dissolved organic nitrogen in water samples.

https://www.sciencedirect.com/science/article/abs/pii/S0043135408002406

The adsorption characteristics of nitrogen in the soils were fitted with different models under different agronomic practices. Fitting could be done using the linear Henry equation in the lower nitrogen balance concentration and with the Freundlich or Langmuir equations in the higher nitrogen balance concentration.

According to the Langmuir equation, the saturated adsorption capacity (Qe) of nitrogen in the soils increased by 1.7%, 14.5%, 18.5% and 7.7% for the soils treated with ploughing, straw returning for 230 days and 350 days, and addition of an impervious agent, respectively, compared with that of the no-tillage treatment. The nitrogen adsorption capacity in ploughed soil increased insignificantly, which may be related to the fact that the plough mainly changed the soil physical properties (e.g., bulk density and permeability) but had no significant effect on the chemical composition and soil colloidal properties.

https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41598-020-71815-z&psig=AOvVaw1ogIBznh9mKr-5al03ns73&ust=1649081794517000&source=images&cd=vfe&ved=0CAsQjRxqFwoTCOiZ1d-K-PYCFQAAAAAdAAAAABAP

I think estimation of nitrate -N in the leached water may be sufficient.Ammonium N may be in very small amount in the leachate. Tests for the presence of nitrate and ammonium-N may be performed in the leachate before experimentation.

The ash sticking to coal char/biochar /charcoal may not contain any nitrogen.The coal materials washings or leachates may contain some basic cations like Ca, Mg, K , Na etc.

Thank you very much Aleksandra Maljković , Prem Baboo , Annangi Subba Rao , for your valuable suggestion.

you can measure total nitrogen using Kjeldahl method.

Thank you all for your precious suggestions!!! and recommendations!!!