The first modern, electronic ternary computer was Setun, built in 1958 in the Soviet Union. It is claimed that it had notable advantages over the binary computers which eventually replaced it, such as lower electricity consumption and lower production cost. But as far as I understand it, the Setun actually used 2 bits to record 1 trit, according to the Google Translated English of the Russian Wikipedia article (
https://ru.m.wikipedia.org/wiki/Сетунь_(компьютер):
"Based on the Gutenmacher binary ferritodiode cell, which is an electromagnetic proximity switch based on transformer-type magnetic amplifiers , N. P. Brusentsov developed a ternary ferritodiode cell [1] [2] , which operated in a two-bit ternary code, i.e. one trit was recorded in two binary digits, the fourth state of two binary digits was not used. ... Two-bit binary encoded ternary digits (2-Bit BinaryCodedTernary, 2B BCT representation, “two-wire”) using all 4 out of 4 possible codes (two out of 4 codes encode the same ternary digit out of 3)."
Maybe the memory used actual trits, while the control logic used bits underneed?
From https://en.wikipedia.org/wiki/Ternary_computer it's not clear to me if there ever were computers that used real ternary logic, instead of just ternary memory and/or ternary logic implemented on top of binary logic.