The statement that is not correct for the periodic classification of elements is :
The first ionization energies along a period do not vary in a regular manner with increase in atomic number
Let us go through each statement.
The properties of elements are the periodic functions of their atomic numbers
This is the statement of the modern periodic law which is perfectly correct.
Atomic size in a period decreases as we move from left to right
This statement is correct. In a period as we move left to right the atomic size decreases as the nuclear charges increases, the force of attraction on the outermost electrons increases, as a result, the size decreases.
The transition elements occupy group 3-12.
This statement is correct as the transition elements are present in groups 3 to 12 of the modern periodic table.
The first ionization energies along a period do not vary in a regular manner with increase in atomic number
This is not true. Ionization energy always increases along a period due to the increase in effective nuclear charge. It gets more and more difficult to remove an electron.