Please refer to Table 450.3(B). The factor to use for primary only protection of transformers with primary currents 9 amperes or less @ 1000V or less is 167%. In you case that would be 1000/208 = 4.8 X 1.67 =8 amperes. Since available fuse ratings are 2, 4. 6. 10. 16, etc., choose 10A and be done with it.
he asked about UL508a, not NEC.
according to the OP, it is a control transformer.
control transformers are dealt with in paragraph 42.
the rated primary current is 1000/208 = 4.8 Amps. the rated secondary current is 1000/120 = 8.33 Amps.
Since he indicated he plans to use both primary and secondary protection, he needs to use table 42.2.
the rating of the primary protection can not exceed 250% of 4.8 Amps or 12 Amps.
the rating of the secondary protection cannot exceed 167% of 8.33 Amps, or 13.91 Amps. You cannot go up to the next standard size. Note "a" only applies when the rated secondary current is 9 Amps or more.
I am pretty sure this is the same as is found in the NEC.