If I understand what you want to do, it doesn't seem like you need two axes.
See below for how to set the YTickLabels correctly.
What exactly do you want in the legend?
% first, I generate some random values for your variables:
Abar = 0.53;
Ubar = 0.2;
Asigma = 0.1;
Usigma = 0.05;
A1 = Abar+Asigma*randn(1,10); % whatever
U1 = Ubar+Usigma*randn(1,10);
%% Figure 1
f1=figure(1);
set(f1,'color','w');
% yyaxis left
% set(gca, 'YTickLabel', {'U1'; 'A1'});
% label1 = {'U1'}
% label2 = {'A1'}
% yyaxis right
% set(gcs,'Ytick',[]);
plot1 = scatter(U1,1,'o','color', [0.7 0 1],'markerfacecolor',[0.7 0 1],'markeredgecolor',[0.7 0 1],'MarkerFaceAlpha',0.5);
hold on
plot2 = scatter(A1,2,'o','color',"b",'markerfacecolor', "b",'markeredgecolor', "b",'MarkerFaceAlpha',0.5);
% hold on
meanA = scatter(Ubar,1,'o','color','r','markerfacecolor','r','markeredgecolor','r','MarkerFaceAlpha',0.7);
meanU = scatter(Abar,2,'o','color','r','markerfacecolor','r','markeredgecolor','r','MarkerFaceAlpha',0.7);
% hold on
plot([Abar Abar],[1.5 3],'r','LineStyle','--','LineWidth',1.5);
plot([Ubar Ubar],[0 1.5],'r','LineStyle','--','LineWidth',1.5);
%Confidence intervals for means
plot([0.0219 0.0219],[1.5 3],'r','LineStyle','--','LineWidth',0.5);
plot([1.0113 1.0113],[1.5 3],'r','LineStyle','--','LineWidth',0.5);
plot([0.1305 0.1305],[0 1.5],'r','LineStyle','--','LineWidth',0.5);
plot([0.2685 0.2685],[0 1.5],'r','LineStyle','--','LineWidth',0.5);
%use error bars to plot std
errorbar([Ubar],[1],Usigma,'horizontal','LineWidth',1)
errorbar([ Abar],[2],Asigma,'horizontal','LineWidth',1)
% ylim([0 3]);
set(gca, 'YLim', [0 3], 'YTick', [1 2], 'YTickLabel', {'U1'; 'A1'});
xlabel('OD');
hold off
