The rare decay $K_L !to! pi^0 u overline{ u}$ was studied with the dataset taken at the J-PARC KOTO experiment in 2016, 2017, and 2018. With a single event sensitivity of $( 7.20 pm 0.05_{rm stat} pm 0.66_{rm syst} ) times 10^{-10}$, three candidate events were observed in the signal region. After unveiling them, contaminations from $K^{pm}$ and scattered $K_L$ decays were studied, and the total number of background events was estimated to be $1.22 pm 0.26$. We conclude that the number of observed events is statistically consistent with the background expectation. For this dataset, we set an upper limit of $4.9 times 10^{-9}$ on the branching fraction of $K_L !to! pi^0 u overline{ u}$ at the 90% confidence level.