*Strengths and Limitations of the Current Review*

In order to ensure high methodological quality, this systematic review and metaanalyses followed the guidelines of the Cochrane Collaboration and PRISMA as well as pre-registering a protocol at PROSPERO. Moreover, a comprehensive search and duplicate full-text study selection, data extraction, and quality assessment were used. Amongst the limitations, we acknowledge that since the search was limited/restricted to English and Scandinavian languages, there might be relevant studies unidentified. Moreover, grey literature was not searched, and thus relevant studies may have been unidentified. Furthermore, the authors of the included studies were not contacted for further information, and the results are merely based on data published in peer-reviewed articles. The review authors were not blinded in the process of selecting literature.

#### **5. Conclusions**

Based on the current low to very low evidence, there seems to be no benefit of providing PUFA supplements to children and adolescents with ADHD concerning parentor teacher-rated core symptoms, behavioral difficulties, or quality of life. Concerns on adverse effects of PUFA supplementation is limited. Conclusive guidance for patients, parent and clinical practice cannot be made due to the many limitations inherent to the included studies.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/ 10.3390/nu13041226/s1, Table S1: the Preferred Reporting Items for Systematic review and Meta-Analysis (PRISMA) checklist, Table S2: Search protocol, Table S3: list of excluded studies, Table S4: Study identification of the included randomized controlled trials, Table S5: The baseline characteristic of the included RCTs, Table S6: The intervention, control, reported outcomes, and authors' conclusion of the included RCTs.

**Author Contributions:** Conceptualization, M.N.H., J.F.R., M.L.R., E.B., K.B., B.T., S.L., H.E.C.; methodology, M.N.H., J.F.R., M.L.R., E.B., K.B., B.T., S.L., H.E.C.; software, not applicable; validation, not applicable; formal analysis, H.E.C.; investigation, M.N.H., J.F.R., M.L.R., E.B., K.B., B.T., S.L., H.E.C.; resources, M.N.H., J.F.R., M.L.R., E.B., K.B., B.T., S.L., H.E.C.; data curation, not applicable; writing—original draft preparation, M.N.H., H.E.C. with contribution from J.F.R., M.L.R., E.B., K.B., B.T., S.L.; writing—review and editing, M.N.H., J.F.R., M.L.R., E.B., K.B., B.T., S.L., H.E.C.; visualization, M.N.H., H.E.C.; supervision, not applicable; project administration, M.N.H., H.E.C.; funding acquisition, M.N.H., J.F.R., M.L.R., E.B., K.B., B.T., S.L., H.E.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** The study was initiated and financed by the Danish Health Authority. The Parker Institute at Bispebjerg and Frederiksberg Hospital was supported by a core grant from the Oak Foundation (OCAY-13-309).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are available at the Danish Health Authority website (www.sst.dk), accessed on 4 April 2021.

**Acknowledgments:** The study was initiated and financed by the Danish Health Authority. The Parker Institute at Bispebjerg and Frederiksberg Hospital was supported by a core grant from the Oak Foundation (OCAY-13-309). The authors would like to thank the work and reference group, as well as the secretary of the "National Clinical Guideline for the Treatment of ADHD in Children and Adolescents", The Danish Health Authority.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
