Manipulate[Module[{sol2},
sol2=ParametricNDSolve[{x'[t]==Cos[t],y'[t]==Sin[t],z'[t]==b*1/4,x[0]==0,y[0]==1,z[0]==0},{x,y,z},{t,0,100},{a}];
ParametricPlot3D[Evaluate[{x[.1][t],y[.1][t],z[.1][t]}/.sol2],{t,1,100},PlotRange->All,BoxRatios->{1,1,10}]],
{b,1,10}]
Not sure what x[][][t], y[][][t], z[][][t]} /. sol2 is supposed to do, but it's currently on the same line as sol2 in your code so it all runs together.