Deep-ultraviolet (DUV) emitters have attracted enormous attentions for water/air purification, and sterilization. However, it is difficult to realize high-efficiency DUV emitters due to several material limitations. In addition, the band mixing effect is another crucial fundamental physics factor limiting device efficiency for 240-260 nm based on AlGaN/AlN quantum wells (QWs). Specifically, heavy hole (HH) and crystal-field split-off (CH) subbands are mixed together in this regime, which results in the insufficient conduction band to valence subband transitions and consequently the low transverse-electric (TE)- and transverse-magnetic (TM)-polarized optical gain. To resolve this issue, we have proposed and investigated the use of AlGaN-delta-GaN and AlN-delta-GaN QWs as active region. Alternatively, high-quality AlGaN substrates are being developed for potential UV applications. However, very limited analysis has been reported for AlGaN QWs on AlGaN substrates. Thus, here, we theoretically study the optical properties of AlGaN QWs on ternary substrates for 240-260 nm. The results show up to 12.16, 7.79 and 6.95 times optical gain enhancements by using AlxGa1-xN/AlyGa1-yN QWs on AlyGa1-yN substrate, as compared to AlxGa1-xN/AlN QWs on AlN substrate at 240 nm, 250 nm and 260 nm, respectively. It can be explained by the fact that the reduced strain in the active region shift HH/CH subbands crossover Al-content to lower Al-content, which ensures the topmost CH subband with large energy separation to HH subband and sufficient C-CH transition. As a result, large TM-polarized optical gain can be achieved, which indicates the great potential of using AlGaN substrate for high-efficiency 240-260 nm lasers.