Will doxycycline affect sprentic birth control pills?

Yes: Birth control pills are all at risk of being affected by antibiotics like doxycycline. You should use a backup form of contraceptive like condoms or abstinence for the rest of this cycle.

No interference: It's an outdated urban myth that antibiotics interfere with effectiveness of birth control pills. They do not, except occasionally with rifampin, an infrequently used antibiotic for certain infections like tuberculosis. Doxycycline certainly has no effect. See https://www.drugs.com/article/antibiotics-and-birth-control.html