The correct answer to this question is option 'A', which is cytoplasmic inheritance. In cytoplasmic inheritance, certain traits are transmitted through the cytoplasm of the cell, specifically through organelles like mitochondria or chloroplasts. These organelles have their own DNA, separate from the nuclear DNA, and are primarily inherited from the mother.

Now let's discuss this in detail:

**Cytoplasmic Inheritance:**
- Cytoplasmic inheritance involves the transmission of genetic traits through the cytoplasm of the cell, rather than through the nuclear DNA.
- The organelles responsible for cytoplasmic inheritance are mitochondria and chloroplasts, which have their own DNA and replicate independently of the nuclear DNA.
- During sexual reproduction, only the mother contributes the cytoplasmic organelles to the offspring, as the sperm contributes only nuclear DNA.
- Therefore, cytoplasmic traits are generally inherited exclusively or predominantly from the mother.

**Maternal Influence in Offspring:**
- Maternal influence refers to the influence of the mother's genetic material on the traits and characteristics of the offspring.
- In general, both parents contribute genetic material to their offspring, but the extent of influence may vary depending on the mode of inheritance.

**Other Modes of Inheritance:**
- Y-linked inheritance: Y-linked traits are inherited exclusively from the father, as they are located on the Y chromosome. Therefore, there is no maternal influence in Y-linked inheritance.
- X-linked inheritance: X-linked traits are carried on the X chromosome. Males have one X chromosome and females have two. In X-linked inheritance, the traits are inherited from both parents, but males are more likely to show the trait if they inherit the mutant allele from their mother. So, while there is some maternal influence in X-linked inheritance, it is not as strong as in cytoplasmic inheritance.
- Autosomal inheritance: Autosomal traits are inherited from both parents equally. There is no specific maternal or paternal influence in autosomal inheritance.

**Conclusion:**
In cytoplasmic inheritance, the organelles responsible for the transmission of genetic traits are inherited exclusively or predominantly from the mother. This results in a greater maternal influence on the offspring's traits. Therefore, in the given options, cytoplasmic inheritance is the mode of inheritance where we expect more maternal influence among the offspring.

In case of cytoplasmic inheritance, distinct maternal effects are observed. This is mainly due to more contribution of cytoplasm to the zygote by female parent than male parent. Generally ovum contributes more cytoplasm to the zygote than sperm. thus,op A.