Is it permissible to pay an annual sum to a sponsor in order to remain under his sponsorship, as a preliminary step to obtaining a government job, knowing that there is no current income?

It is not permissible for the guarantor to take money in exchange for their guarantee. However, if the stay of the guaranteed person in the country depends on giving money to the guarantor, there is no harm in that, because it is a means for them to attain their right, similar to what is paid to acquire a right or repel an injustice.