In minimal polynomial, . . . . . . . . degree polynomial is present with coefficients in the basefield along with the zeros in extension field.

The correct answer is C. Smallest.

A minimal polynomial is a polynomial with coefficients in a field $F$ that has a root in an extension field $K$ of $F$, and such that no polynomial with coefficients in $F$ with a root in $K$ has a smaller degree.

In other words, a minimal polynomial is the polynomial of smallest degree that has a root in the extension field.

For example, the minimal polynomial of $\sqrt{2}$ over $\mathbb{Q}$ is $x^2 - 2$, since this is the polynomial of smallest degree that has $\sqrt{2}$ as a root.

The other options are incorrect.

A is incorrect because the minimal polynomial is not necessarily the largest degree polynomial with coefficients in the base field along with the zeros in extension field. For example, the minimal polynomial of $\sqrt{2}$ over $\mathbb{Q}$ is $x^2 - 2$, which is not the largest degree polynomial with coefficients in $\mathbb{Q}$ that has $\sqrt{2}$ as a root.

B is incorrect because the minimal polynomial is not necessarily a constant polynomial. For example, the minimal polynomial of $\sqrt{2}$ over $\mathbb{Q}$ is $x^2 - 2$, which is not a constant polynomial.

D is incorrect because the minimal polynomial is not necessarily unpredictable. For example, the minimal polynomial of $\sqrt{2}$ over $\mathbb{Q}$ is $x^2 - 2$, which is a predictable polynomial.