  The study of open charm meson production provides an efficient tool for the
investigation of the properties of hot and dense matter formed in
nucleus-nucleus collisions. The interpretation of the existing di-muon data
from the CERN SPS suffers from a lack of knowledge on the mechanism and
properties of the open charm particle production. Due to this, the heavy-ion
programme of the \NASixtyOne experiment at the CERN SPS has been extended by
precise measurements of charm hadrons with short lifetimes. A new Vertex
Detector for measurements of the rare processes of open charm production in
nucleus-nucleus collisions was designed to meet the challenges of track
registration and high resolution in primary and secondary vertex
reconstruction. A small-acceptance version of the vertex detector was installed
in 2016 and tested with Pb+Pb collisions at 150\AGeVc. It was also operating
during the physics data taking on Xe+La and Pb+Pb collisions at 150\AGeVc
conducted in 2017 and 2018. This paper presents the detector design and
construction, data calibration, event reconstruction, and analysis procedure.
