Chinese immigrants faced various legal restrictions that limited their rights in the United States, particularly during the late 19th and early 20th centuries. Specifically, the Chinese Exclusion Act of 1882 significantly restricted Chinese immigration and included provisions that effectively barred Chinese immigrants from becoming U.S. citizens. This lack of citizenship meant that they could not vote, testify in court, or own property.
The restrictions you've mentioned primarily applied during the territorial era as well as the years that followed the Chinese Exclusion Act until changes in immigration laws and civil rights movements began to dismantle these restrictions. Therefore, the correct option aligns with "during the territorial era" given that many of these restrictions were enforced in the latter half of the 19th century.
In summary, the most accurate period relating to the legal discrimination against Chinese immigrants in regards to voting, testifying in court, and property ownership would be during the time of the Chinese Exclusion Act and its effects, which aligns with your option of "during the territorial era."