On the Extended Class of SUPM and Their Generating URSM Over Non-Archimedean Field

In this article, we investigate an extended class of strong uniqueness polynomial over non-Archimedean field than that was recently studied by Khoai-An [ $$p$$ -Adic Numb. Ultrametr. Anal. Appl. 12 (4), 276–284 (2020)]. We also find the unique range set of weight 2 corresponding to the SUPM which improve and generalize significantly the results of the paper of Khoai-An [ $$p$$ -Adic Numb. Ultrametr. Anal. Appl. 12 (4), 276–284 (2020)] and an earlier one due to Hu-Yang [Acta Math. Viet. 24 (1), 95–108 (1999)].