This work studies the product and ratio statistics of independent and non-identically distributed (i.n.i.d.) α−κ−μ shadowed random variables. We derive the series expression for the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) of the product and ratio of i.n.i.d. α−κ−μ shadowed random variables. We then give the single integral representation for the derived PDF expressions. Further, as application examples, 1) outage probability has been derived for cascaded wireless systems, and 2) physical-layer security metrics like secrecy outage probability and strictly positive secrecy capacity are derived for the classic three-node model with α−κ−μ shadowed fading. Next, we discuss an intelligent reflecting surface-assisted communication system over α−κ−μ shadowed fading.