Question about controlling for categorical covariate in one-sample t-test(SPM)

Dear all,

I have a question about how to control for the categociral covariate effect in one-sample t-test
I have a cross-over design in which participants overall experience condition 1 though 5 in an event-related manner but, experience condition B after A
for, example, they go through conditions A1, A2, A3, A4,A5(randomized) then, B1,B2,B3,B4,B5(randomized)
and this order was counterbalanced between participants. (some people experienced condition A first then B , some people experienced condition B first then A)

I set up a parametric regressor for condition 1 ~ 5 and want to test the parametric regressor effect for contrast A>B,
but I want to control for the effect of A, B order.
since this order covariate is a categorical variable, I dummy coded it( 1 , 0 : 1 for A->B order participants, and 0 for B->A order participants) and put it as a covariate in the second level one sample t-test without centering it (*no centering option), and put [1 0 ] as contrast weight.

Is this the right way to control for the order effect in one-sample t-test in spm?

Just to make sure I have coded it reversely ( 0 , 1 : 0 for A->B order, and 1 for B->A order), and this changes the results…
It seems like dummy coding it sets a certain reference level… but what I want to do it control for the order effect not check the difference between differently ordered groups…

How would I do this in SPM?
should I set the option to center to Overall Mean?

any advice would be of great help,

thank you very much in advance.