The insufficient coverage of cervical cytology screening in underdeveloped countries or remote areas is currently the bottleneck hurdle to its widespread implementation. Conventional centralized medical screening methods are heavily dependent on sizable, costly investments as well as sufficient qualified pathologists. In this paper, we have developed a cervical precancerous assisted-screening system for identifying high-risk squamous intraepithelial lesion (SIL) cases in regions with limited resources. This system utilizes a low-cost miniature microscope and a low-pathologist-reliance artificial intelligence algorithm. We design a low-cost compact microscope with pixel resolution about 0.87 mm/pixel for imaging cytology slides. To tackle the challenge of sparely-distributed lesion cells in cytology whole slide images (WSIs), we have developed a dual-stage slide classification model. In first stage, we train an instance-level classifier by self-supervised pretraining on large-number unlabeled cervical images and transfer learning on small-number labeled images, aiming to reduce negative cells within a slide. In the second stage, we employ our proposed Att-Transformer, which aggregates deep features extracted from the top 200 lesion probabilities instances, for slide-level classification. We train and validate our model on 3,510 low-resolution WSIs collected from four different centers, and evaluate our model on 364 slides from two external centers in remote areas, achieving AUC (area under receiver operating characteristic curve) of 0.87 and 0.89 respectively for screening high risk cases. We also evaluate it on new independent cohorts of 391 slides from the original four centers and achieve AUC of 0.89. Overall, all the results indicate that integration of our innovative algorithm together with the compact microscope represents a promising approach to cervical cytology precancerous screening for high-risk population in medical resource limited regions. This affordable and accessible screening is significant as it contributes towards the goal of eliminating cervical cancer worldwide.