Although words like 'first' and 'largest' were used in the paper by Chia-Feng Yang and colleagues  (open-access available here) observing that "AD [atopic dermatitis] and asthma with allergic sensitization are associated with ADHD [attention-deficit hyperactivity disorder] in children", I'm minded to be a little cautious with such 'we're the first/best' assertions.
Cautious because, on quite a few peer-reviewed research occasions (see here for example), a possible *link* between various allergic disease and ADHD has already been noted; even potentially extending to studies talking about how treatment for allergic disease might on some occasions also impact on presented ADHD symptoms (see here) (with no medical advice given or intended).
Yang et al relied on data from a research favourite country, Taiwan, derived from an initiative called the Childhood Environment and Allergic diseases Study (CEAS). The clue is in the name of the initiative in terms of what they were looking for/at, as per other publications derived from the initiative . From the 3200-odd participants eligible for participation, researchers relied on data from over 2700 children. Questions about allergic disease history were asked to parents of said participants, alongside other 'environmental' factors such as family income, tobacco exposure and breastfeeding history. I note also a question about 'incensing at home' is also included relating to the use of burning incense typically linked to religious practices in certain cultures.
When it came to a diagnosis of ADHD, it's not entirely clear about how this was ascertained but it looks like diagnosis was given by a clinician: "The conditions of disease in children were confirmed by board-certified child psychiatrists or pediatric neurologists, according to the clinical evaluation." I should also mention that participants also received skin prick tests (SPTs) covering a range of potential allergens: "house dust mites (HDMs mix, including Der p, Der f, Der m, and Blot allergens), cockroaches, dog dander, milk, egg, and crab allergens" as way of defining allergic sensitisation.
Results: there was a "strong positive association between ADHD and allergic sensitization as diagnosed by positive SPTs." In other words, despite finding a fairly low level of ADHD in their sample (1%), those who 'reacted' to one or more of the allergens tested for via the skin prick test seemed to be at some increased risk of ADHD. Such an enhanced risk spanned both those presenting with "AD with allergic sensitization and asthma with allergic sensitization."
The authors provide some further results and details on the possible hows-and-whys of their results. Obviously the immune system figures quite strongly given what for example, they were testing for with the SPT and their focus on AD and asthma. The word 'inflammation' also figures quite heavily. I note too that the authors reiterate previous suggestions that: "Control of allergens exposure might be a critical factor influencing the development of ADHD."
There is a further scheme of work to follow in this area, not just dealing with mechanisms but also in relation to 'treating' allergies also potentially 'treating' [some] ADHD. I say this on the basis that other independent research has observed that before reaching for the antihistamine as a potential ADHD-modifier, there may actually be a connection between early antihistamine exposure and the development of ADHD  (albeit with potential confounders) to keep in mind. Other work also supporting a link between ADHD and atopic disease  provides some other 'clues' that may require further investigation; not least "cow's milk intolerance", which ties into similar findings (see here) and could also be one route from which ADHD heightens the risk of subsequent future psychiatric disorder (see here) in light of other 'milk' associations (see here).
 Yang CF. et al. Association between allergic diseases, allergic sensitization and attention-deficit/hyperactivity disorder in children: A large-scale, population-based study. J Chin Med Assoc. 2017 Nov 24. pii: S1726-4901(17)30304-0.
 Wang IJ. et al. Allergens, air pollutants, and childhood allergic diseases. Int J Hyg Environ Health. 2016 Jan;219(1):66-71.
 Schmitt J. et al. Increased attention-deficit/hyperactivity symptoms in atopic dermatitis are associated with history of antihistamine use. Allergy. 2017 Oct 4.
 Hak E. et al. Association of childhood attention-deficit/hyperactivity disorder with atopic diseases and skin infections? A matched case-control study using the General Practice Research Database. Ann Allergy Asthma Immunol. 2013 Aug;111(2):102-106.e2.