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We are reporting on analysis, design, construction, and key parameters of the device for a two-way time transfer via an optical fiber. The dominant source of errors in the two-way optical time transfer (TWOTT) via relatively short optical fibers is the temperature dependence of internal delays within the terminal units. We have performed an analysis of the influence of the internal delays and their temperature dependence on the TWOTT process considering two different configurations of the terminals with the feedback coupling in optical and electrical domains. The achieved results have been used for the optimal design of a TWOTT system implementing standard small form-factor pluggable optical transceivers. The operational tests of this new TWOTT system confirmed the precision of the time transfer on the subpicosecond level, the time transfer stability characterized by TDEV better than 60 fs for averaging intervals …