Crossover designs are of the type in which sequence of different treatments are administered one at a time over a certain period of time, during which the presence of residual effect or rather carryover effect can longer be ignored. This paper therefore presents two first order residual effect, that is effect on the immediate next period after the period of treatment application. The first method constructs designs for any number of treatment, v for any prime number that has x=2 as primitive root of the associated Galois field. using the two algorithms I₁ = ( x⁰, x^m , x^2m,..., x^2k-x)and I₂ = (x¹, x^m+1, x^2m+1,..., x^2k-x+1). The second method is also for the construction of designs for any number treatment, v for any prime number that has x=3 as the primitive root of the corresponding Galois field with two algorithms I₁ = (x⁰, x^m, x^2m,..., x^2k+m-x-1) and I₂ = (x¹, x^m+1, x^2m+1,..., x^2k+m-x). By exploiting cyclic development of v-1 initial sequences of treatment order, universally optimal balanced crossover design of the first order for the two methods were constructed in this paper and the two methods generate every non-zero elements of any prime number.