Context. Extreme high-synchrotron peaked blazars (EHSPs) are rare high-energy sources characterised by synchrotron peaks beyond 1017 Hz in their spectral energy distributions (SEDs). Their extreme properties challenge conventional blazar emission models and provide a unique opportunity to test the limits of particle acceleration and emission mechanisms in relativistic jets. However, the number of identified EHSPs is still small, limiting comprehensive studies of their population and characteristics. Aims. This study aims to identify new EHSP candidates and characterise their emission properties, including synchrotron peak frequencies, Compton dominance, and jet environments. It also examines how EHSPs fit within the broader framework of the blazar sequence, providing insights into their role in the population of active galactic nuclei. Methods. A sample of 124 γ-ray blazars was analysed, selected for their high synchrotron peak frequencies and γ-ray emission properties, with a focus on sources showing low variability and good broadband data coverage. Their SEDs were constructed using archival multi-wavelength data from the SSDC SED Builder service, supplemented with recent Swift-UVOT, Swift-XRT, and Fermi-LAT observations. The SEDs were modelled with a one-zone synchrotron/synchrotron-self-Compton framework, classifying sources by synchrotron peak frequency. EHSP properties are compared to other blazar populations, and their detectability with the Cherenkov Telescope Array Observatory (CTAO) is assessed. Results. We identify 66 new EHSP candidates, significantly expanding the known population. A clear correlation between synchrotron peak frequency and the magnetic-to-kinetic energy density ratio is found, with the most extreme EHSPs nearing equipartition. This indicates that as the synchrotron peak shifts to higher frequencies, the energy stored in the magnetic field becomes comparable to that of the relativistic electrons, suggesting a more balanced and energetically efficient jet environment in the most extreme blazars. Host galaxy emission is detected in many sources, but no significant differences are observed between elliptical and lenticular hosts. Finally, our analysis suggests that nine high-synchrotron peaked/EHSPs could be observed by CTAO at >5σ (20 at >3σ) in 20-hour exposures, a feasible integration time for Imaging Atmospheric Cherenkov Telescopes, indicating that while the overall detection rate remains modest, a subset of these sources is within reach of next-generation very-high-energy gamma-ray instruments.