Father brought half piece of land can owner force to buy the remaining

My father purchased a piece of land from a layer around 15 years ago, now he has started construction on that land (actually a home to live) that is in village because we do not have proper house. The problem is that my father didn't bought the whole piece of that land because of money at that time, now the person asking him to either purchase the whole piece of land (left part + some govt. land near to road which he stating that its his piece of land but during measuring its cleared that belongs to state govt.) or I will disturb you. Now he lodged two cases through his peoples not directly and he is telling that if we do not purchase the whole piece of land that he is demanding he will lodge some more cases. We have problem that we have less money that is either we can complete our construction or we con fulfill his demand and if we go for construction we have to deal with those cases and also we have to prepare for the cases that he will lodge. Thank you