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The recent exquisite Gaia astrometric, photometric, and radial velocity (RV) measurements resulted in a substantial advancement for the determination of the orbits for old star clusters, including the oldest Milky Way globular clusters (MW GCs). The main goal of this paper is to use the Gaia DR3 and the VVVX measurements to obtain the orbits for nearly a dozen new Galactic GC candidates that have been poorly studied or previously unexplored. We use the Gaia DR3 and VVVX databases to identify bonafide members of the Galactic GC candidates: VVV-CL160, Patchick122, Patchick125, Patchick126, Kronberger99, Kronberger119, Kronberger143, ESO92-18, ESO93-08, Gaia2, and Ferrero54. The relevant mean cluster physical parameters are derived (distances, Galactic coordinates, proper motions, RVs). We measure accurate mean RVs for the GCs VVV-CL160 and Patchick126, using observations acquired at the Gemini-South telescope with the IGRINS high-resolution spectrograph. Orbits for each cluster are then computed using the GravPot16 model, assuming typical Galactic bar pattern speeds. We reconstruct the orbits for these clusters for the first time. These include star clusters with retrograde and prograde orbital motions, both in the Galactic bulge and disk. Orbital properties, such as the mean time-variations of perigalactic and apogalactic distances, eccentricities, vertical excursions from the Galactic plane, and Z-components of the angular momentum are obtained for our sample. Our main conclusion is that, based on the orbital parameters, Patchick125 and Patchick126 are genuine MW bulge/halo GCs; Ferrero54, Gaia2 and Patchick122 are MW disk GCs. The orbits of Kronberger99, Kronberger119, Kronberger143, ESO92-18, and ESO93-08 are more consistent with old MW disk open clusters. VVV-CL160 falls very close to the Galactic centre, but reaches larger distances beyond the Sun, thus its origin is still unclear.