An autotopism Θ = (α, β, γ) of a partial Latin square P = (p) with symbols in N = {0, 1, …, n − 1} is said to be a Santilli’s autotopism of P if there exist j ∈ N such that α(i) = p, β(i) = p and γ(i) = p, for all i ∈ N. In this paper, we are interested in the set SPLS (Θ) of partial Latin squares having Θ as a Santilli’s autotopism. Specifically, the cardinality of the set of minimal elements of SPLS(Θ) is obtained and a classification of Latin squares Santilli’s isotopisms of order ≤ 5 fixing at least one symbol is given.