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Context. The recent and exquisite astrometric, photometric, and radial velocity measurements of the Gaia mission resulted in a substantial advancement of the determination of the orbits for old star clusters, including the oldest Milky Way globular clusters (MW GCs). Aims. The main goal of the present paper is to use the new Gaia data release 3 (DR3) and the VISTA Variables in the Via Láctea Extended Survey (VVVX) measurements to obtain the orbits for nearly a dozen new MW GC candidates that have been poorly studied or previously unexplored. Methods. We use the Gaia DR3 and VVVX databases to identify bona fide MW GC candidates, namely VVV-CL160, Patchick 122, Patchick 125, Patchick 126, Kronberger 99, Kronberger 119, Kronberger 143, ESO 92-18, ESO 93-08, Gaia 2, and Ferrero 54. The relevant mean cluster physical parameters are derived (distances, Galactic coordinates, proper motions, radial velocities). We also measure accurate mean radial velocities for the GCs VVV-CL160 and Patchick 126 using observations acquired at the Gemini-South telescope with the Immersion GRating INfrared Spectrometer (IGRINS) high-resolution spectrograph. Orbits for each cluster are then computed using the GravPot16 model, assuming typical Galactic bar pattern speeds. Results. We reconstruct the orbits for these 11 star clusters for the first time. These include star clusters with retrograde and prograde orbital motions, both in the Galactic bulge and disk. We obtain orbital properties for this sample, 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. Conclusions. Our main conclusion is that, based on the orbital parameters, Patchick 125 and Patchick 126 are genuine MW bulge or halo GCs; and Ferrero 54, Gaia 2, and Patchick 122 are MW disk GCs. In contrast, the orbits of Kronberger 99, Kronberger 119, Kronberger 143, ESO 92-18, and ESO 93-08 are more consistent with old MW disk open clusters, in agreement with previous results. VVV-CL160 falls very close to the Galactic centre, but reaches larger distances beyond the Solar orbit, and therefore its origin is still unclear.