The application of semi-quantum key distribution (SQKD) facilitates the development of semi-quantum technology, and semi-quantum signature (SQS) schemes emerged. However, there is no relatively complete security analyses of SQS schemes like SQKD protocols in existing works. Motivated by the four-particle cluster states and semi-quantum cryptography, we propose a novel semi-quantum co-signature (SQCS) scheme based on GHZ states and four-particle cluster states. Meanwhile, we provide the relatively complete security analyses of SQS schemes. In addition, the analyses indicate that the proposed SQCS scheme under limited resources is more secure and effective than some typical quantum signature (QS) schemes and SQS schemes.