Consider a hyperbolic or an elliptic quadric Qϵ (3, q), ϵ ∈ {+, −}, in PG(3, q) and let Eϵ denote the set of all lines of PG(3, q) that are external with respect to Qϵ (3, q). If π is a (tangent or secant) plane of PG(3, q), then π Qϵ (3, q) is an Eϵ-blocking set which is minimal, except when (q, ϵ) = (2, +) and π is a secant plane. In this way, we obtain two families of (minimal) blocking sets of sizes mϵ1 and mϵ2, with (m+1, m+2) = (q2 − q, q2 ) and (m−1, m−2) = (q2, q2 + q), where those of size mϵ1 are also the minimum size Eϵ-blocking sets. Motivated by the search for new (families of ) minimal Eϵ-blocking sets with sizes in the open interval ]mϵ1, mϵ2[, we determine here all Eϵ-blocking sets of size mϵ1 + 1 in PG(3, q) in the case q ∈ {2, 3}.