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The cross sections of the 𝑒+𝑒−→𝜙𝜂′ process at center-of-mass energies from 3.508 to 4.951 GeV are measured with high precision using 26.1 fb−1 data collected with the BESIII detector operating at the BEPCII storage ring. The cross sections are of the order of a few picobarn and decrease as the center-of-mass energy increases as 𝑠−𝑛/2 with 𝑛=4.35±0.14. This result is in agreement with the Nambu-Jona-Lasinio model prediction of 𝑛=3.5±0.9. In addition, the charmless decay 𝜓(3770)→𝜙𝜂′ is searched for by fitting the measured cross sections, yet no significant signal is observed. The upper limit of ℬ(𝜓(3770)→𝜙𝜂′) at the 90% confidence level is determined to be 2.3×10−5.