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We present the selection, spectroscopic identification, and physical properties of extreme emission line galaxies (EELGs) at $3<z<3.7$ aiming at studying physical properties of an analog population of star-forming galaxies (SFGs) at the epoch of reionization. The sample is selected based on the excess in the observed Ks broad band flux relative to the best-fit stellar continuum model flux. By applying a 0.3 mag excess as a primary criterion, we select 240 EELG candidates with intense emission lines and estimated observed-frame equivalent width (EW) of $\gtrsim 1000$ angstrom over the UltraVISTA-DR2 ultra-deep stripe in the COSMOS field. We then carried out a HK band follow-up spectroscopy for 23 of the candidates with Subaru/MOIRCS, and find that 19 and two of them are at $z>3$ with intense [OIII] emission, and H$α$ emitters at $z\simeq 2$, respectively. These spectroscopically identified EELGs at $z\simeq 3.3$ show, on average, higher specific star formation rates (sSFR) than the star-forming main sequence, low dust attenuation of $E(B-V) \lesssim 0.1$ mag, and high [OIII]/[OII] ratios of $\gtrsim 3$. We also find that our EELGs at $z\simeq 3.3$ have higher hydrogen ionizing photon production efficiencies ($ξ_\mathrm{ion}$) than the canonical value ($\simeq 10^{25.2}$ Hz/erg), indicating that they are efficient in ionizing their surrounding interstellar medium. These physical properties suggest that they are low metallicity galaxies with higher ionization parameters and harder UV spectra than normal SFGs, which is similar to galaxies with Lyman continuum (LyC) leakage. Among our EELGs, those with the largest [OIII]/[OII] and EW([OIII]) values would be the most promising candidates to search for LyC leakage.