There are factors governing the selectivity of the most appropriate method used: the functional group of the organic substance, its molecular mass and then its particle size, the nature of the water where the targeted organic substance exists (pH, temperature, industrial water or domestic water i.e. chemical compositions of the water ..etc). So, initially specify the kind of water and the targeted organic substance to remove. Here are some useful links that help further to answer the question:
I also highly recommend reading this patent (https://patents.google.com/patent/US20150056692A1/en) where a unique method was used: reducing specific organic substances (BTEX) from water using a specific kind of peaceful bacteria, and then you may contact my previous supervisor, Prof. Muftah El-Naas, Muftah El-Naas https://www.researchgate.net/profile/Muftah-El-Naas, for further information.
Organic compounds can be removed from water by adsorption, coagulation/flocculation, ion exchange and oxidation processes. Adsorption is the most commonly used process for organic compound removal from water and uses a variety of adsorbents such as activated carbon, alumina, silica gel and resins. In regenerative systems, the adsorption mechanism is usually based on the physical and chemical interactions between the adsorbent and the organic compounds. The adsorbent material can be regenerated by elution with a suitable solvent, such as methanol, to remove the organic compounds from the adsorbent.