Context. The discovery and characterization of mini-Neptunes hold a potentially crucial impact on planetary formation and evolution theories. Estimating their orbital parameters and atmospheric properties would provide valuable hints to improve formation and atmospheric models. Aims. We present the discovery of two mini-Neptunes near a 2:1 orbital resonance configuration orbiting the K0 star TOI-1803. We describe in detail their orbital architecture and suggest some possible formation and evolution scenarios. Methods. Using CHEOPS, TESS, and HARPS-N datasets, we estimated the radius and the mass of both planets. We used a multidimensional Gaussian process with a quasi-periodic kernel to disentangle the planetary components from the stellar activity in the HARPS-N dataset. We performed dynamical modeling to explain the orbital configuration and performed planetary formation and evolution simulations. For the least dense planet, we assumed different atmospheric compositions and defined possible atmospheric scenarios with simulated JWST observations. Results. TOI-1803 b and TOI-1803 c have orbital periods of ∼6.3 and ∼12.9 days, respectively, residing in close proximity to a 2:1 orbital resonance. Ground-based photometric follow-up observations have revealed significant transit timing variations (TTV) with an amplitude of ∼10 min and ∼40 min, respectively, for planets b and -c. With the masses computed from the radial velocities dataset, we obtained a density of (0.39 ± 0.10) ρ⊕ and (0.076 ± 0.038) ρ⊕ for planets b and -c, respectively. TOI-1803 c is among the least dense mini-Neptunes currently known, and due to its inflated atmosphere, it is a suitable target for transmission spectroscopy with JWST. With NIRSpec observations, we could understand whether the planet has kept its primary atmosphere or not, which would constrain our formation models. Conclusions. We report the discovery of two mini-Neptunes close to a 2:1 orbital resonance. The detection of significant TTVs from ground-based photometry opens scenarios for a more precise mass determination. TOI-1803 c is one of the least dense mini-Neptunes known so far, and it is of great interest among the scientific community since it could constrain current formation scenarios. JWST observations could give us valuable insights to characterize this interesting system. ★This study uses CHEOPS data observed as part of the Guaranteed Time Observation (GTO) program CH_PR100031 and the observations made with the Italian Telescopio Nazionale Galileo (TNG) operated by the Fundación Galileo Galilei (FGG) of the Istituto Nazionale di Astrofisica (INAF) at the Observatorio del Roque de los Muchachos (La Palma, Canary Islands, Spain).