"In summary, there is evidence that n-3 PUFAs [polyunsaturated fatty acids] supplementation monotherapy improves clinical symptoms and cognitive performances in children and adolescents with ADHD [attention-deficit hyperactivity disorder], and that these youth have a deficiency in n-3 PUFAs levels."
So said the results of the systematic review and meta-analysis published by JanePei-Chen Chang and colleagues  taking in the collected peer-reviewed research literature on the topic of fatty acids and ADHD. This continues a research theme down the years suggesting that said compounds might be beneficial for at least some people diagnosed with ADHD (see here) and screening for signs of omega-3 fatty acid deficiency could be preferentially clinically indicated for those diagnosed or at risk of a diagnosis.
I don't want to dwell too much on the results because (a) they speak for themselves and (b) this is an area of science that has been a talking point for quite a few years. I know there has been a degree of 'over-hype' associated with fatty acids down the ages but as part of a larger scheme of work suggesting that food and nutrition are not so detached from some behavioural/developmental diagnoses (see here for another example) I'm minded to suggest that they are given their due credit. Certainly fatty acid supplements are quite inexpensive and also seemingly useful for various aspects of physical health too.
As to the mode of effect, well, we don't know all there is to know just yet. I note that some of the authors on the Chang paper are not adverse to the idea that something like psychiatry and immune functions are linked (see here). Whether at least some cases of ADHD might be accompanied by more 'inflammatory' issues is still the source of some debate; although I'd be quick to add in the quite voluminous research suggesting that allergy and ADHD might have more than a passing relationship (see here). Is is possible that supplementation with specific types of fatty acids typically labelled as 'anti-inflammatory'  could be working as anti-inflammatory agents? Well, possibly, but I daresay there may be other biological processes at work too. More research is indicated but the Chang results provide yet more [strong] evidence that at least some of those with ADHD may benefit from a fish oil or two a day.
And whilst on the topic of fatty acids, I might also direct you to an interesting piece of research recently published by Sheppard and colleagues ...
 Chang JC. et al. Omega-3 Polyunsaturated Fatty Acids in Youths with Attention Deficit Hyperactivity Disorder (ADHD): A Systematic Review and Meta-Analysis of Clinical Trials and Biological Studies. Neuropsychopharmacology. 2017 Jul 25.
 Wall R. et al. Fatty acids from fish: the anti-inflammatory potential of long-chain omega-3 fatty acids. Nutr Rev. 2010 May;68(5):280-9.
 Sheppard KW. et al. Effect of Omega-3 and -6 Supplementation on Language in Preterm Toddlers Exhibiting Autism Spectrum Disorder Symptoms. J Autism Dev Disord. 2017. July 26.