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BP Psc is an active late-type (sp:G9) star with unclear evolutionary status lying at high galactic latitude $b=-57^{\circ}$. It is also the source of the well collimated bipolar jet. We present results of the proper motion and radial velocity study of BP Psc outflow based on the archival $Hα$ imaging with the GMOS camera at 8.1-m Gemini-North telescope as well as recent imaging and long-slit spectroscopy with the SCORPIO multi-mode focal reducer at 6-m BTA telescope of SAO RAS. The 3D kinematics of the jet revealed the full spatial velocity up to $\sim$140 km$\cdot$s$^{-1}$ and allows us to estimate the distance to BP Psc system as $D=135\pm40$ pc. This distance leads to an estimation of the central source luminosity $L_*\approx1.2L_{\odot}$, indicating that it is the $\approx$1.3$M_{\odot}$ T Tauri star with an age $t\lesssim$ 7 Myr. We measured the electron density of order $N_e\sim10^2$ cm$^{-3}$ and mean ionization fraction $f\approx0.04$ within the jet knots and estimated upper limit of the mass-loss rate in NE lobe as $\dot{M}_{out}\approx1.2\cdot10^{-8}M_{\odot}\cdot yr^{-1}$. The physical characteristics of the outflow are typical for the low-excitation YSO jets and consistent with the magnetocentrifugal mechanism of its launching and collimation. Prominent wiggling pattern revealed in $Hα$ images allowed us to suppose the existence of a secondary substellar companion in a non-coplanar orbit and estimate its most plausible mass as $M_p\approx 30M_{Jup}$. We conclude that BP Psc is one of the closest to the Sun young jet-driving systems and its origin is possibly related to the episode of star formation triggered by expanding supershells in Second Galactic quadrant.