The highest and the lowest melting point of elements in Group $13$  are of respectively

Non-metals have higher melting points than that of metals

Correct option :

(3) Boron is a non-metal. It is a property of non-metals that they have higher melting points in comparison to the metals of their group. Hence, the melting point of Boron is much higher in comparison to the other members of the group $13$ While, Gallium has an unusual structure due to which, it has the lowest melting point and highest melting point. It suggests that the liquid form of Gallium is more stable than the solid form. Hence, it has the lowest melting point. Therefore, this option is correct.

Incorrect options :

(1) Due to the property of non-metals, boron has the highest melting point. But, since we already know that Gallium has the lowest melting point and not Aluminum, this pair doesn't represent the elements with the lowest and the highest melting points. Hence, this option is incorrect.

(2)Thallium and Boron have the highest and lowest melting points respectively. But the element with the highest melting point is boron and not thallium. Hence,  the option is incorrect.

(4) Boron has the highest melting point in the group $13$ due to the property of non-metals as we have discussed above. But, Thallium isn't the element having the lowest melting point. As we have already discussed, Gallium has the lowest melting point, not Thallium. Hence, this option is incorrect.

Boron has the highest melting point and Gallium has the lowest melting point. 

Therefore, the correct answer is option (3).