成品代码：

public class xbk {
    public static String signSha256WithRSA(String value) {
        try {
            Signature signature = Signature.getInstance("SHA256withRSA");
            String key = "MIIEpAIBAAKCAQEAxXtnv7W6k44w12+hPdFQ1Tg0s8TmSpqftyn2NxM/NPL0eDxz+twU440lJyWC3B1vzH1WpXw/l+vSjtKcQV1UWAlKVrdPrsIDJiuh7NEXfDHdd/JPnYqHIZsjWM9pMUQPv2atq1tT02grj5CRBq2xAL5zShhcOIAgi+yGcOIdoO1IHJpEBHaZnHuMm6wVDy48d46/0euNJCWIsomqe4ltj5/s/lPzpUPSA9doJtQmzEaK56y1jlMGkX5vkteNwtSib2wG8neh3q2iezU0PvNsXomHiksANadPyXN3YqIHalBMIQt/iXfo+tfqbSPEAK4OC4A934jqcpywXy76K/RAAQIDAQABAoIBAHJF5ZQesZceyY5wbwpZa//lpUF9J5F2BgO0SWA3R/T4vZQxzx8TaRb/nscXQrDia8YVpSTfT+E2OcIhhv+f5OWIgrbJHlfOtonI58skdwWLyU7WLVHJTkaZAgwrAQDcFIy5+rbUgx4rAkHx8qm9qlX23rm6fOrI4Yx2UplRjrmGcAi5tHnRS8fGJuud2Pco7L1J4cNwhUILWqbttoxKlR21hOhH3SEMCqe6trR6NsOqHwsBA0todoKGBvw3FKgNzML9eRvIaCVojrgEVyUfwULkw8SMneYWu339J9cFYq8EB7Uo9qjVo9nLRsag2zScck5sL7pdBWIioB8Hs8GGJQECgYEA7ODBYUvCSBxjjHjQznsSUKHH/xOwkAOVCCy5xJj2riU9ld3oEh3laxuJDcF52K5KOHz3l8/thJYZpVebh6rzSMb9pTVD4pMtGMZMY629kp2IMh2gIHy1kon6gXYhG/W8jadB11Et1m047RQDqlkKesSdHph1Q0PEQIZ81O5l4VECgYEA1WyBuLdbFgA0oa18n2pUsZxB+7oam8tcrHCPGnAVYYwvu/lZ1z+TaLmR2UAamwiL998J8POBJtRuzebrhlNErbr3biGc1v9MJywVLZRbVWmPDLZmnBBfbmkVyHwiBd4RxzPvgHJ6EGWYqtSWkPQhp8P/flyc1QSZw2nagGQmR7ECgYEAzM6nZNBz8pVZHSN4po6Sj1TR7yG/D0WJnb/N/sWiw38/eEydUsy2h50PKu2VxFstoRmrmX8WBgUht2u/9dVA9DPZKvaa81P9MeaCNc0Kk7HRCEPFJ1GsTD8wcK8KgXo+xNtQejKeRz+4cINVh/vkq7FDiCiZesck8AVX+WMGg4ECgYBYJQ9Sdc/Vv1H9cERnJqhCDpIl4A/7RjtJMNe5iI8cEaTpUqurPaOo/fNhsZsLarU8M07MyBUQL25v9a5SdPOJeQ2V26YGGbye9RLuFza9iPI+wtqQHCb918LaYYI/wB7Bkg6Zky4ctYkfDNv+lAWOX2GXE7LmO5cx4PcQTcyNkQKBgQCNX8fZb+PRF9/qZKxH31kAY3dx1rxI+7Ufx5l1aAzwSt6RIi9HRIyEzkMOqnq+Eo+gxOfP/Ot3DpMHCeBG8Vh35PrQpT7l2yiaxZEC+/Ee5tv6ooTpAFSHiPhg3YZnECF/wMSChe7loxFMLNZ6MDihpquPaRHuU+QoDV2wcppdQQ==";
            signature.initSign(KeyFactory.getInstance("RSA").generatePrivate(new PKCS8EncodedKeySpec(Base64.getDecoder().decode(key))));
            signature.update(value.getBytes());
            return Base64.getEncoder().encodeToString(signature.sign());
        } catch (Exception e) {
            e.printStackTrace();
        }
        return "";
    }

    public static void main(String[] args) {
        System.out.println(signSha256WithRSA("11"));
    }
}