We report the results of spectroscopic observations , obtained with the Gemini North Multi-Object Spectrograph , of 9 planetary nebulae ( PNe ) and 15 H ii regions located in the 5.5 ^ { \prime } \times 5.5 ^ { \prime } inner region of the nearby starburst galaxy IC10 . Twelve new candidate PNe have been discovered during our pre-imaging phase . Nine of them have been spectroscopically confirmed . The direct availability of the electron temperature diagnostics in several nebulae allowed an accurate determination of the metallicity map of IC10 at two epochs : the present-time from H ii regions and the old/intermediate-age from PNe . We found a non-homogeneous distribution of metals at both epochs , but similar average abundances were found for the two populations . The derived age-metallicity relation shows a little global enrichment interpreted as the loss of metals by SN winds and to differential gas outflows . Finally , we analyzed the production of oxygen –through the third dredge-up– in the chemical abundance patterns of the PN populations belonging to several dwarf irregular galaxies . We found that the third dredge-up of oxygen is a metallicity dependent phenomenon occurring mainly for 12+ \log ( O/H ) \leq 7.7 and substantially absent in IC10 PNe .