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Recently, in Innamorati and Zuanni (J. Geom 111:45, 2020.  10.1007/s00022-020-00557-0 ) the authors give a characterization of a Baer cone of    $$\mathrm {PG}(3, q^2)$$  PG ( 3 , q 2 ) ,  q  a prime power, as a subset of points of the projective space intersected by any line in at least one point and by every plane in    $$q^2+1$$  q 2 + 1 ,    $$q^2+q+1$$  q 2 + q + 1 or    $$q^3+q^2+1$$  q 3 + q 2 + 1 points. In this paper, we show that a similar characterization holds even without assuming that the order of the projective space is a square, and weakening the assumptions on the three intersection numbers with respect to the planes.

On Baer cones in $$\mathrm {PG}(3, q)$$