We introduce here the AdaptSgenoLasso, a new penalized likelihood method for gene mapping and for genomic prediction, which is an extended version of the SgenoLasso. The AdaptSgeno-Lasso relies on the original concept of a selective genotyping that varies along the genome. The "classical" selective genotyping on which the SgenoLasso is built on, consists in genotyping only extreme individuals, in order to increase the signal from genes. However, since the same amount of selection is applied at all genome locations, the signal is increased of the same proportional factor everywhere. With the AdaptSgenoLasso, we allow geneticists to impose more weights on some loci (i.e. locations) of interest, known to be responsible for the variation of the quantitative trait. The resulting signal is now dedicated to each locus. We propose here a deep theoretical study of the AdaptSgenoLasso, and we show on simulated data the superiority of this new approach over the SgenoLasso.