Which of the following statements is correct ?

To determine the correct statement, let us analyze each option in detail:

1. Fusion of two cells is called Karyogamy:
This statement is incorrect. Karyogamy refers specifically to the fusion of two nuclei during sexual reproduction. The fusion of the protoplasms of two cells is called plasmogamy.

2. Fusion of protoplasms between two motile on non-motile gametes is called plasmogamy:
This statement is correct. Plasmogamy is the first stage of sexual reproduction in fungi and other organisms, where the protoplasms of two motile or non-motile gamete cells fuse together without the fusion of their nuclei.

3. Organisms that depend on living plants are called saprophytes:
This statement is incorrect. Organisms that feed on or depend on living plants or animals are called parasites. Saprophytes are organisms that obtain their nutrients from dead and decaying organic matter.

4. Some of the organisms can fix atmospheric nitrogen in specialized cells called sheath cells:
This statement is incorrect. Certain cyanobacteria (like Nostoc and Anabaena) can fix atmospheric nitrogen in specialized, thick-walled cells called heterocysts, not sheath cells.

Therefore, the only correct statement is that the fusion of protoplasms between two motile on non-motile gametes is called plasmogamy.