Magnetic skyrmions can be generated, destroyed and driven to motion by electric spin currents in metals based on the spin transfer torque (STT) mechanism. However, the STT technique does not work in insulating materials because no electric currents can pass through. Fortunately, the magnetoelectric (ME) interaction that is present in multiferroic insulators makes it possible to manipulate magnetic skyrmions by applying electric fields. We have recently simulated ferroelectric (FE) skyrmionic crystals (or skyrmionic lattices so that skyrmionic crystals can be abbreviated as SkLs) formed in two-dimensional (2D) ferromagnetic (FM) multiferroic materials. Antiferromagnets are more abundant in nature. For this reason, we employ here a quantum computational method which we have developed in recent years to investigate the magnetic and polarized electric dipole textures of a 2D antiferromagnetic (AM) multiferroic system. Consequently, we observe in simulations that antiferroelectric (AE) and AM skyrmionic crystals can be generated simultaneously in a broad temperature and magnetic field phase region. Each of these AM and AE SkLs can be decomposed into two ferromagnetic or ferroelectric lattices which are FM or FE SkLs respectively, an FE skyrmion in one FE SkL is an electric dipole complex formed around the interstitial site of another FE SkL. The topological charges of the FE skyrmions are quantized to be integers, half integers or the odd multiples of ±0.25 especially within subsequently normally applied electric fields. In a strong external magnetic field, AE SkL and AM vortical crystal (VL) usually coexist. A subsequently applied perpendicular electric field is able to stabilize or destroy the both sorts of SkLs, and considerably elevate the coexisting temperatures of the AE SkL and AM VL textures even the electric field is very weak.