1. My sister and I took part in school marathon yesterday.
2. My sister and I took part in a school marathon yesterday.
3. My sister and I took part in the school marathon yesterday.
4. My sister and I took part in School Marathon yesterday.
5. My sister and I took part in the School Marathon yesterday.
6. My sister and I took part in a School Marathon yesterday.
(Which expressions are grammatical?)
If you mean your school's one and only school marathon, then 3 is correct.
If you mean one of many schools' marathons, then 2 is correct.
The others are incorrect.