The ones that have red berries off the top of my head are;
Heteromeles arbutifolia
Pyracantha coccinia
Nandina domestica
Or some type of Cotoneaster such as Cotoneaster dammeri. I would need to see more of the plant. Does it have thorns? How big is it?
Cotoneaster (pronounced /kəˈtoʊniːˈæstər/)[3] is a genus of woody plants in the rose family, Rosaceae, native to the Palaearctic region (temperate Asia, Europe, north Africa), with a strong concentration of diversity in the genus in the mountains of southwestern China and the Himalayas.[4] They are related to hawthorns (Crataegus), firethorns (Pyracantha), photinias (Photinia) and rowans (Sorbus).
Depending on the species definition used, there are between 70 to 300 different species of cotoneaster, with many apomictic microspecies treated as species by some authors, but only as varieties by others.[4][5]
The majority of species are shrubs from 0.55 metres (1.616 ft) tall, varying from ground-hugging prostrate plants to erect shrubs; a few, notably C. frigidus, are small trees up to 15 metres (49 ft) tall and 75 centimetres (30 in) trunk diameter. The prostrate species are mostly alpine plants growing at high altitude (e.g. C. integrifolius, which grows at 3,0004,000 metres (9,80013,000 ft) in the Himalayas), while the larger species occur in scrub and woodland gaps at lower altitudes.
The shoots are dimorphic, with long shoots (1040 centimetres/3.916 inches long) producing structural branch growth, and short shoots (0.55 centimetres/0.202.0 inches long) bearing the flowers; this pattern often developing a 'herringbone' form of branching. The leaves are arranged alternately, 0.515 centimetres (0.205.9 in) long, ovate to lanceolate, entire; both evergreen and deciduous species occur. The flowers are produced in late spring through early summer, solitary or in corymbs of up to 100 together. The flower is either fully open or has its five petals half open 510 millimetres (0.200.39 in) diameter. They may be any shade from white through creamy white to light pink to dark pink to almost red, 10-20 stamens and up to five styles. The fruit is a small pome 512 millimetres (0.200.47 in) diameter, pink or bright red, orange or even maroon or black when mature, containing one to three (rarely up to five) seeds.[5][6] Fruit on some species stays on until the following year.