In the number fields setting, the deepest and most mysterious invariants in arithmetic are conjecturally captured by the so-called « motivic cohomology ». Mordell-Weil groups, class groups, group of units and values of L-functions are some examples. The most obscure definition of motivic cohomology is build as extension groups in the hypothetical category of mixed motives, but this definition is almost unreachable and mathematicians in the field rather use pieces of K-theory. This talk will be devoted to portray the analogous picture in the function fields setting, using mixed (uniformizable) Anderson $A$-motives instead of classical mixed motives. We will compute the extension groups and define the $A$-motivic cohomology in this setting. In addition, we shall discuss the notion of extensions having everywhere good reduction, analogous to the classical definition of Scholl.