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[abridged]The aim of this work is to search for planets around evolved stars,with a special focus on stars more massive than 2\,M$_\odot$ in light ofprevious findings that show a drop in planet occurrence around stars above thismass. We used \texttt{kima} to find the Keplerian orbits most capable ofexplaining the periodic signals observed in RV data. We also studied thevariation of stellar activity indicators and photometry in order to discardstellar signals mimicking the presence of planets. We present a planetcandidate in the open cluster NGC3680 that orbits the 1.64\,M$_\odot$ star No.41. The planet has a minimum mass of 5.13M\,$_{J}$ and a period of 1155 days.We also present periodic and large-amplitude RV signals of probable stellarorigin in two more massive stars (5.84 and 3.05\,M$_\odot$ in the clustersNGC2345 and NGC3532). Finally, using new data, we revise the RV signals of thethree stars analysed in our previous paper. We confirm the stellar origin ofthe signals observed in NGC2423 No. 3 and NGC4349 No. 127. On the other hand,the new data collected for IC4651 No. 9122 (1.79\,M$_\odot$) seem to supportthe presence of a bona fide planet of 6.22M\,$_{J}$ at a period of 744 days,although more data will be needed to discard a possible correlation with theCCF-FWHM. The targets presented in this work showcase the difficulties ininterpreting RV data for evolved massive stars. The use of several activityindicators (CCF-FWHM, CCF-BIS, \ha), photometry, and long-term observations(covering several orbital and stellar rotational periods) is required todiscern the true nature of the signals. However, in some cases, all thisinformation is insufficient, and the inclusion of additional data -- such asthe determination of magnetic field variability or RV points in thenear-infrared -- will be necessary to identify the nature of the discoveredsignals.

Planets around evolved intermediate-mass stars III. Planet candidates and long-term activity signals in six open clusters