To solve this problem, we need to evaluate each statement to determine which one is correct.$\newline$Let's analyze each option:$\newline$• Option 1: Fusion of two cells is called Karyogamy.$\newline$ - Karyogamy refers specifically to the fusion of nuclei, not entire cells. Therefore, this statement is incorrect.$\newline$• Option 2: Fusion of protoplasms between two motile or non-motile gametes is called plasmogamy.$\newline$ - Plasmogamy is indeed the fusion of the cytoplasm (protoplasm) of two gametes, which can be either motile or non-motile. This statement is correct.$\newline$• Option 3: Organisms that depend on living plants are called saprophytes.$\newline$ - Saprophytes are organisms that feed on dead or decaying organic matter, not living plants. Organisms that depend on living plants are typically parasites. This statement is incorrect.$\newline$• Option 4: Some of the organisms can fix atmospheric nitrogen in specialized cells called sheath cells.$\newline$ - Nitrogen fixation typically occurs in specialized cells called heterocysts in some cyanobacteria, not sheath cells. This statement is incorrect.$\newline$Therefore, the correct statement is Option 2: Fusion of protoplasms between two motile or non-motile gametes is called plasmogamy.