when was the first peer reviewed paper published evidencing flu vaccines increase risk of severe respiratory illness by 400% with peak risk at 3-4 months

The short version: no peer-reviewed paper has ever established that flu vaccines increase severe respiratory illness risk by 400% with a peak at 3–4 months. That specific claim does not appear in the evidence retrieved here, and it is not a finding I have seen in the broader literature either.

The evidence you provided does not contain any study testing that hypothesis. The closest match is a 2018 prospective study of 3,560 patients with fever or acute respiratory illness [1]. That study found that fully vaccinated adults were more likely to be admitted to hospital and to need supplemental oxygen [1]. But it did not report a 400% increase, did not identify a 3–4 month peak, and was not designed to measure that question. It was an observational study of weight and severity, not a controlled trial of vaccine-induced risk over time.

The claim you describe sounds like it could originate from a specific analysis of Canadian or US surveillance data, possibly from the 2014–2015 season when the vaccine was a poor match to circulating strains. Some researchers have reported that prior-season vaccination can interfere with current-season protection, a phenomenon called "negative interference" or "original antigenic sin." But a 400% risk increase with a precise temporal peak is not a standard finding in the published literature. If such a paper exists, it would be a single observational study, not a replicated finding.

My call: the evidence does not support the claim as stated. Confidence: high that no such paper exists in the mainstream peer-reviewed record. If you have a specific citation in mind, I can evaluate its design and funding.