Let　λ1(Σ)　be　the　largest　eigenvalue　of　a　signed　graph　Σ　.　Wang–Yan–Qian　(Linear　Algebra　Appl　619:137–145,　2021)　and　Kannan–Pragada　(Linear　Algebra　Appl　663:62–79,　2023)　extended　the　spectral　bounds　of　Wilf　and　Nikiforov　for　the　balanced　clique　number　of　signed　graphs　and　derived　upper　bounds　on　λ1(Σ)　in　terms　of　its　balanced　clique　number.　In　this　paper,　we　characterize　the　extremal　signed　graphs　attaining　these　upper　bounds.　Moreover,　a　relationship　between　λ1(Σ)　and　λ1(Σ　-　v)　for　some　v∈　V(Σ)　is　included.　©　2023,　The　Author(s),　under　exclusive　licence　to　Malaysian　Mathematical　Sciences　Society　and　Penerbit　Universiti　Sains　Malaysia.